Yiannis Sakellaridis, Ali Baklouti, Taro Yoshino (#1), Gen Mano (#1), Joseph Bernstein (#1), Joseph Bernstein (#2) (4 lectures), Tilmann Wurzbacher (6 lectures), Peter Trapa, Herve Sabourin, R. Stanton, Taro Yoshino (#2), Masatoshi Iida, Tomoyuki Arakawa, Gen Mano (#2), Chifune Kai, Nobutaka Boumuki, Soji Kaneyuki, KarlHermann Neeb, Yoshishige Haraoka, Salem Ben Saïd, Pablo Ramacher, Michaël Pevzner (#1), Michaël Pevzner (#2) (4 lectures), Hisayosi Matumoto, Masayasu Moriwaki, Kyo Nishiyama, Junko Inoue, Noriyuki Abe,
Date:  February 6 (Tue), 2007, 16:3017:30 
Room:  RIMS, Kyoto University : Room 402 
Speaker:  Yiannis Sakellaridis (Tel Aviv) 
Title:  On the spectrum of spherical varieties over padic fields 
Abstract: [pdf] 
Spherical varieties are a very important class of spaces which includes all symmetric varieties. Over a padic field, their representation theory seems to admit some description through a "Langlands dual" group. I will discuss results on the unramified component of their spectrum which point to this direction. If time permits, I will show how this theory can be used to obtain a completely general CasselmanShalika formula for eigenfunctions of the Hecke algebra on an arbitrary spherical variety. 
Date:  February 8 (Thu), 2007, 10:0011:00 
Room:  RIMS, Kyoto University : Room 402 
Speaker:  Ali Baklouti (Sfax) 
Title:  On Hardy's Theorem on nilpotent Lie groups 
Abstract: [pdf] 
It is well known that Hardy's uncertainty principle for R^{n} was generalized to connected and simply connected nilpotent Lie groups. In this work, we extend it further to connected nilpotent Lie groups with noncompact centre. We show however that Hardy's theorem fails for a connected nilpotent Lie group which is not simply connected. 
Date:  February 8 (Thu), 2007, 11:1512:15 
Room:  RIMS, Kyoto University : Room 402 
Speaker:  Taro Yoshino (吉野太郎) (RIMS) 
Title:  Deformation spaces of compact CliffordKlein forms of homogeneous spaces of Heisenberg groups 
Abstract: [pdf] 
T. Kobayashi introduced the deformation space of CliffordKlein forms, which is a natural generalization of deformation spaces of geometric structures. SelbergWeil's local rigidity theorem claims that the deformation space is discrete for Riemannian irreducible symmetric spaces M if the dimension d(M) ≥ 3. In contrast to this theorem, Kobayashi proved that local rigidity does not hold (even in higher dimensional case) in the nonRiemannian case. Then, this opens a new problem to find explicity such deformation spaces in high dimensions. However, such explicit forms have not been obtained except for a few cases now. In this talk, I will give an explicit description of the deformation spaces of compact CliffordKlein forms of homogeneous spaces of Heisenberg groups. 
Date:  February 8 (Thu), 2007, 12:1513:00 
Room:  RIMS, Kyoto University : Room 402 
Speaker:  Gen Mano (真野元) (RIMS) 
Title:  The unitary inversion operator for the minimal representation of the indefinite orthogonal group O(p,q) 
Abstract: [pdf] 
The L^{2}model of the minimal representation of the indefinite orthogonal group O(p,q) (p+q even, greater than four) was established by KobayashiØrsted (2003). In this talk, we present an explicit formula for the unitary inversion operator, which plays a key role for the analysis on this L^{2}model. Our proof uses the Radon transform of distributions supported on the light cone. 
Date:  February 14 (Wed), 2007, 10:0011:30 
Room:  RIMS, Kyoto University : Room 005 
Speaker:  Joseph Bernstein (Tel Aviv) 
Title:  On the support of the Plancherel measure 
Abstract: [pdf] 
In 1970s Harish Chandra finished his work on harmonic analysis on
real reductive groups G. In particular, he proved the Plancherel formula for
G which describes the decomposition of the regular representation of G as an
integral of irreducible unitary representations of the group G × G
(Plancherel decomposition).
The remarkable feature of this formula was the fact that only some of the unitary representations of the group Gcontributed to this formula (so called tempered representations). In fact this phenomenon was already known in PDE. Namely in this case it was known that one can describe the spectral decomposition of an elliptic selfadjoint differential operator D in terms of eigenfunctions which have moderate growth (i.e. they almost lie in L^{2}). The general result of this sort was proven by Gelfand and Kostyuchenko in 1955. In my paper "On the support of Plancherel measure" (1988) I have applied the ideas of Gelfand and Kostyuchenko and gave an a priori proof of the fact that only tempered representations contribute to the Plancherel decomposition. Moreover, I have shown that a similar statement holds for decompositions of L^{2}(X) for a large class of homogeneous Gspaces X. Examples are: (i) X = G/K, where K is the maximal compact subgroup (ii) more generally, X = G/H, where H is a symmetric subgroup (subgroup of fixed points of some involution of G); (iii) X = G/Γ, where Γ is a discrete lattice in G. (iv) G a reductive padic group, X = G/H, where H is either an open compact subgroup or a symmetric subgroup. I have discovered that the corresponding statement depends on some geometric structure on the space X (I called it "the structure of large scale space") and that this structure has the same properties in all the cases listed above. In my lecture I will discuss all these questions. 
Date: 
February 9 (Fri), 2007, 10:0011:30 February 13 (Tue), 2007, 13:0014:30 February 16 (Fri), 2007, 10:0011:30 February 20 (Tue), 2007, 13:0014:30 
Room:  RIMS, Kyoto University : Room 402 
Speaker:  Joseph Bernstein (Tel Aviv) 
Title:  Applications of representation theory to problems in analytic number theory (mini course) 
Abstract: [pdf] 
In this minicourse I will describe a general approach which allows
to use methods of analytic representation theory in order to prove some highly
nontrivial estimates in analytic number theory.
This minicourse is based on my works with Andre Reznikov. I will study representations of the group G = SL(2,R) (and closely related groups) in the space of functions on the automorphic space X = Γ\G. My aim is to describe relations of this problem to analytic number theory and to show how using methods of representation theory one can get very powerful estimates of different quantities important in number theory. The plan of the minicourse. Abstract. In this lecture I will discuss automorphic forms and Maass forms on upper halfplane. I will show that many problems about such forms are better expressed in the language of automorphic representations. I will illustrate this on the model example which gives bounds for Sobolev norms of the automorphic functional. Abstract. I will discuss the problem of estimates for triple product of automorphic functions and its connection to estimates of automorphic Lfunctions. Using the language of automorphic representations described in first lecture I will show how to explain the exponentially decaying factor in the triple product and then I will describe how to prove the convexity bound for these products. I will continue the investigation of triple products and show how one can prove a nontrivial subconvexity bound for triple products using a combination of geometric and spectral estimates. 
Date: 
March 7 (Wed), 2007, 10:0011:30 (Room 005) March 8 (Tur), 2007, 10:0011:30 (Room 005) March 9 (Fri), 2007, 10:0011:30 (Room 402) March 13 (Tue), 2007, 10:0011:30 (Room 402) March 14 (Wed), 2007, 10:0011:30 (Room 005) March 16 (Fri), 2007, 10:0011:30 (Room 402) 
Room:  RIMS, Kyoto University : Room 005 and 402 
Speaker:  Tilmann Wurzbacher (Metz) 
Title:  Coisotropic actions (mini course) 
Abstract: [pdf] 
The first aim of this course is to explain the context and the
basic properties of coisotropic actions of Lie groups on symplectic manifolds
(i.e. actions having generically coisotropic orbits), as well as of spherical
varietes (i.e. complexalgebraic varieties with an action of a complex reductive
Lie group such that all Borel subgroups thereof have an open orbit). After
interludes on geometric quantization resp. on lagrangian actions, we prove the
equivalence of the two above conditions in the complexalgebraic setup.
Finally, we give applications of this theorem to, e.g., geometric quantization
of Kähler manifolds and remark on connections to related subjects.
I. Symplectic reminders II. Geometric quantization in 90 minutes III. Lagrangian actions IV. Coisotropic actions V. Applications, remarks and outlook For details, see the pdf file. 
Date:  March 13 (Tue), 2007, 16:3017:30 
Room:  RIMS, Kyoto University : Room 402 
Speaker:  Peter Trapa (Utah, USA) 
Title:  On the Matsuki correspondence for sheaves 
Abstract: [pdf] 
Suppose G is a real reductive group with maximal compact subgroup K. Let X denote the flag variety for the complexified Lie algebra of G, and let K_{C} denote the complexification of K. Nearly thirty years ago, Matsuki established an orderreversing bijection between the sets of K_{C} and G orbits on X. Later MirkovicUzawaVilonen extended this to an equivalence of K_{C}equivariant and Gequivariant sheaves on X (a result originally conjectured by Kashiwara). Meanwhile, to each such kind of sheaf, Kashiwara showed how to attach a Lagrangian cycle in the cotangent bundle of X. Composing this characteristic cycle construction with the MirkovicUzawaVilonen equivalence, one obtains an isomorphism between the topdimensional homology of the conormal variety for K_{C} orbits on X and the topdimensional homology of the conormal variety for G orbits on X. Schmid and Vilonen proved that this isomorphism is compatible with the KostantSekiguchi correspondence of nilpotent orbits. The purpose of this talk is to give a finer explicit computation of a suitable "leading part" of the isomorphism in homology. 
Date:  March 20 (Tue), 2007, 16:3017:30 
Room:  RIMS, Kyoto University : Room 402 
Speaker:  Herve Sabourin (Universite de Poitiers) 
Title:  Unipotent representations of a real simple Lie group attached to small nilpotent orbits 
Abstract: [pdf] 
It is a classical idea of Kirillov and Kostant that irreducible representations of a real simply connected Lie group G are related to the orbits of G in the dual g* of its Lie algebra. When G is nilpotent, we know that there is a bijection between the set of Gcoadjoint orbits and the unitary dual \widehat{G} of G. When G is solvable, a similar correspondence is due to Auslander and Kostant. For other groups, there are complications even with regard to what is true. Let us suppose now that G is simple and let O be a coadjoint orbit. If O is semisimple, there is a natural way to associate to O an unitary representation Π(O), but the problem is much more difficult if O is nilpotent. Nevertheless, when O is a minimal nilpotent orbit, one can define a notion of representation "associated" to O and develop a strategy to construct explicitly Π(O). Our goal is to show how this strategy can be extended to the non minimal case and what kind of new results it yields. 
Date:  March 23 (Fri), 2007, 10:3011:30 
Room:  RIMS, Kyoto University : Room 402 
Speaker:  R. Stanton (Ohio) 
Title:  Symplectic constructions for extraspecial parabolics 
Abstract: [pdf] 
The minimal nilpotent orbit in a simple, say, complex Lie algebra has interaction with several topics. In work joint with M. Slupinski, we are investigating the Heisenberg grading associated to any element of the orbit. Röhrle ['93] referred to the corresponding JacobsonMorozov parabolic as an extraspecial parabolic, and parametrized the orbits of the Levi subgroup acting on the nilradical modulo the center. Using exclusively methods from symplectic geometry, we shall reexamine this representation of the Levi subgroup. We shall classify orbits using the moment map; examine the symplectic nature of each of the orbits; give symplectic constructions of distinguished subgroups that occur in Rubenthaler's list of reductive dual pairs. In particular, we give a symplectic construction of the exceptional simple group G_{2}. 
Date:  April 24 (Tue), 2007, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Taro Yoshino (吉野太郎) (University of Tokyo) 
Title:  Existence problem of compact CliffordKlein forms of the infinitesimal homogeneous space of indefinite Stiefle manifolds 
Abstract: [ pdf ] 
The existence problem of compact CliffordKlein forms is important in the study of discrete groups. There are several open problems on it, even in the reductive cases, which is most studied. For a homogeneous space of reductive type, one can define its 'infinitesimal' homogeneous space. This homogeneous space is easier to consider the existence problem of compact CliffordKlein forms. In this talk, we especially consider the infinitesimal homogeneous spaces of indefinite Stiefel manifolds. And, we reduce the existence problem of compact CliffordKlein forms to certain algebraic problem, which was already studied from other motivation. 
Date:  May 1 (Tue), 2007, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Masatoshi Iida (飯田正敏) (Josai University) 
Title:  HarishChandra expansion of the matrix coefficients of P_{J} Principal series Representation of Sp(2,R) 
Abstract: [ pdf ] 
Asymptotic expansion of the matrix coefficents of class1 principal series representation was considered by HarishChandra. The coefficient of the leading exponent of the expansion is called the cfunction which plays an important role in the harmonic analysis on the Lie group. In this talk, we consider the HarishChandra expansion of the matrix coefficients of the standard representation which is the parabolic induction with respect to a nonminimal parabolic subgroup of Sp(2,R). This is the joint study with Professor T. Oda. 
Date:  May 8 (Tue), 2007, 17:0018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Tomoyuki Arakawa (荒川知幸) (Nara Women's University) 
Title:  Affine Walgebras and their representations 
Abstract: [ pdf ] 
The Walgebras are an interesting class of vertex algebras, which can be understood as a generalization of Virasoro algebra. It was originally introduced by Zamolodchikov in his study of conformal field theory. Later FeiginFrenkel discovered that the Walgebras can be defined via the method of quantum BRST reduction. A few years ago this method was generalized by KacRoanWakimoto in full generality, producing many interesting vertex algebras. Almost at the same time Premet rediscovered the finitedimensional version of Walgebras (finite Walgebras), in connection with the modular representation theory. In the talk we quickly recall the FeiginFrenkel theory which connects the Whittaker models of the center of U(g) and affine (principal) Walgebras, and discuss their representation theory. Next we recall the construction of KacRoanWakimoto and discuss the representation theory of affine Walgebras associated with general nilpotent orbits. In particular, I explain how the representation theory of finite Walgebras (=the endmorphism ring of the generalized GelfandGraev representation) applies to the representation of affine Walgebras. 
Remark:  この週は同氏による集中講義 14:4016:40 があります。 セミナーの時刻はいつもと違いますのでご注意ください。 
Date:  May 17 (Thu), 2007, 15:0016:30 
Place:  Room 002, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Gen Mano (真野 元) (University of Tokyo) 
Title:  The unitary inversion operator for the minimal representation of the indefinite orthogonal group O(p,q) 
Abstract: [ pdf ] 
The indefinite orthogonal group O(p,q) (p+q even, greater than four) has a distinguished infinite dimensional irreducible unitary representation called the 'minimal representation'. Among various models, the L^{2}model of the minimal representation of O(p,q) was established by KobayashiØrsted (2003). In this talk, we focus on and present an explicit formula for the unitary inversion operator, which plays a key role for the analysis on this L^{2}model as well as understanding the Gaction on L^{2}(C). Our proof uses the Radon transform of distributions supported on the light cone. This is a joint work with T. Kobayashi. 
Remark:  いつもと時刻・部屋が違います。ご注意ください。 
Date:  May 22 (Tue), 2007, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Chifune Kai (甲斐千舟) (Kyushu University) 
Title:  A characterization of symmetric cones by an orderreversing property of the pseudoinverse maps 
Abstract: [ pdf ] 
When a regular open convex cone is given, a natural partial order is introduced into the ambient vector space. If we consider the cone of positive numbers, this partial order is the usual one, and is reversed by taking inverse numbers in the cone. In general, for every symmetric cone, the inverse map of the associated Jordan algebra reverses the order. In this talk, we investigate this orderreversing property in the class of homogeneous convex cones which is much wider than that of symmetric cones. We show that a homogeneous convex cone is a symmetric cone if and only if the order is reversed by the Vinberg's *map, which generalizes analytically the inverse maps of Jordan algebras associated with symmetric cones. Actually, our main theorem is formulated in terms of the family of pseudoinverse maps including the Vinberg's *map as a special one. While our result is a characterization of symmetric cones, also we would like to mention O. Güler's result that for every homogeneous convex cone, some analogous pseudoinverse maps always reverse the order. 
Date:  May 25 (Fri), 2007, 14:3016:00 
Place:  Room 122, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Nobutaka Boumuki (坊向伸隆) (Osaka City University, Advanced Mathematical Institute) 
Title:  The classification of simple irreducible pseudoHermitian symmetric spaces: from a view of elliptic orbits 
Abstract: [ pdf ]  In this talk, we call a special elliptic element an Sprelement, we create an equivalence relation on the set of Sprelements of a real form of a complex simple Lie algebra, and we classify Sprelements of each real form of all complex simple Lie algebras under our equivalence relation. Besides, we demonstrate that the classification of Sprelements under our equivalence relation corresponds to that of simple irreducible pseudoHermitian symmetric Lie algebras under Berger's equivalence relation. In terms of the correspondence, we achieve the classification of simple irreducible pseudoHermitian symmetric Lie algebras without Berger's classification. 
Date:  May 25 (Fri), 2007, 16:0017:30 
Place:  Room 122, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Soji Kaneyuki (金行壯二) 
Title:  Causalities, Gstructures and symmetric spaces 
Abstract: [ pdf ] 
Let M be an ndimensional smooth manifold, F(M) the frame bundle of M, and let G be a Lie subgroup of GL(n,R). We say that M has a Gstructure, if there exists a principal subbundle Q of F(M) with structure group G. Let C be a causal cone in R^{n}, and let AutC denote the automorphism group of C. Starting from a causal structure \mathcal{C} on M with model cone C, we construct an AutCstructure Q(\mathcal{C}). Several concepts on causal structures can be interpreted as those on AutCstructures. As an example, the causal automorphism group Aut(M,\mathcal{C}) of M coincides with the automorphism group Aut(M,Q(\mathcal{C})) of the AutCstructure. As an application, we will consider the unique extension of a local causal transformation on a Cayley type symmetric space M to the global causal automorphism of the compactification of M. 
Date:  May 29 (Tue), 2007, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  KarlHermann Neeb (Technische Universität Darmstadt) 
Title:  A host algebra for the regular representations of the canonical commutation relations 
Abstract: [ pdf ] 
We report on joint work with H. Grundling (Sydney). The concept of a host algebra generalises that of a group C *algebra to groups which are not locally compact in the sense that its nondegenerate representations are in onetoone correspondence with representations of the group under consideration. A full host algebra covering all continuous unitary representations exist for an abelian topological group if and only if it (essentially) has a locally compact completion. Therefore one has to content oneselves with certain classes of representations covered by a host algebra. We show that there exists a host algebra for the set of continuous representations of the countably dimensional Heisenberg group corresponding to a nonzero central character. 
Remark:  Neeb 教授は５月２６日（土）・２７日（日）に 東京大学で行われる第２回高木レクチャーで招待講演をされます。 こちらもどうぞご参加ください。 
Date:  June 19 (Tue), 2007, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Yoshishige Haraoka (原岡喜重) (Kumamoto University) 
Title:  Rigid local systems, integral representations of their sections and connection coefficients 
Abstract: [ pdf ] 
A local system on CP^{1}{finite points} is called physically rigid if it is uniquely determined up to isomorphisms by the local monodromies. We explain two algorithms to construct every physically rigid local systems. By applying the algorithms we obtain integral representations of solutions of the corresponding Fuchsian differential equation. Moreover we can express connection coefficients of the equation in terms of the integrals. These results will be applied to several differential equations arising from the representation theory. 
Date:  June 29 (Fri), 2007, 15:3016:30, 16:4517:45 
Place:  Room 122, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Salem Ben Saïd (Université Henri Poincaré  Nancy 1) 
Title:  On the theory of Bessel functions associated with root systems 
Abstract: [ pdf ] 
The theory of spherical functions on Riemannian symmetric spaces G/K and on noncompactly causal symmetric spaces G/H has a long and rich history. In this talk we will show how one can use a limit transition approach to obtain generalized Bessel functions on flat symmetric spaces via the spherical functions. A similar approach can be applied to the theory of HeckmanOpdam hypergeometric functions to investigate generalized Bessel functions related to arbitrary root system. We conclude the talk by giving a conjecture about the nature and order of the singularities of the Bessel functions related to noncompactly causal symmetric spaces. 
Date:  October 2 (Tue), 2007, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Pablo Ramacher (Göttingen University) 
Title:  Invariant integral operators on affine Gvarieties and their kernels 
Abstract: [ pdf ] 
We consider certain invariant integral operators on a smooth affine variety M carrying the action of a reductive algebraic group G, and assume that G acts on M with an open orbit. Then M is isomorphic to a homogeneous vector bundle, and can locally be described via the theory of prehomogenous vector spaces. We then study the Schwartz kernels of the considered operators, and give a description of their singularities using the calculus of bpseudodifferential operators developed by Melrose. In particular, the restrictions of the kernels to the diagonal can be described in terms of local zeta functions. 
Date:  October 9 (Tue), 2007, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Michaël Pevzner (Université de Reims and University of Tokyo) 
Title:  RankinCohen brackets and covariant quantization 
Abstract: [ pdf ] 
The particular geometric structure of causal symmetric spaces permits the definition of a covariant quantization of these homogeneous manifolds. Composition formulae (#products) of quantizad operators give rise to a new interpretation of RankinCohen brackets and allow to connect them with the branching laws of tensor products of holomorphic discrete series representations. 
Date:  October 25 (Thu), 2007, 16:3018:00 October 30 (Tue), 2007, 15:0016:30 November 1 (Thu), 2007, 16:3018:00 November 6 (Tue), 2007, 15:0016:30 
Place:  Room 126 (on Tuesdays) or 052 (on Thursdays), Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Michaël Pevzner (Université de Reims and University of Tokyo) 
Title:  Quantization of symmetric spaces and representation 
Abstract: [ pdf ] 
The goal of this series of lectures will be to describe and compare two intimately related but nevertheless fundamentally different methods of quantization of symmetric spaces : on the one hand deformation quantization and symbolic calculus on the other hand. We shall also discuss interesting connections with the representation theory of semisimple Lie groups. Undergraduate students are welcome.
The first and introductory lecture of a series of four will be devoted to the discussion of fundamental principles of the Quantum mechanics and their mathematical formulation. This part is not essential for the rest of the course but it might give a global vision of the subject to be considered. We shall introduce the Weyl symbolic calculus, that relates classical and quantum observables, and will explain its relationship with the socalled deformation quantization of symplectic manifolds. Afterwards, we will pay attention to a more algebraic question of formal deformation of an arbitrary smooth Poisson manifold and will define the Kontsevich starproduct. Lecture 2: Back to Mathematics. Two methods of quantization. We'll start with a discussion on
Lecture 3: Kontsevich's formality theorem and applications in Representation theory. We shall first give
Lecture 4: The last lecture will be devoted to following subjects:

Date:  October 30 (Tue), 2007, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Hisayosi Matumoto (松本久義) (University of Tokyo) 
Title:  On Weyl groups for parabolic subalgebras 
Abstract: [ pdf ] 
Let ${\mathfrak g}$ be a complex semisimple Lie algebra. We call a parabolic subalgebra ${\mathfrak p}$ of ${\mathfrak g}$ normal, if any parabolic subalgebra which has a common Levi part with ${\mathfrak p}$ is conjugate to ${\mathfrak p}$ under an inner automorphism of ${\mathfrak g}$. For a normal parabolic subalgebra, we have a good notion of the restricted root system or the little Weyl group. We have a comparison result on the Bruhat order on the Weyl group for ${\mathfrak g}$ and the little Weyl group. We also apply this result to the existence problem of the homomorphisms between scalar generalized Verma modules. 
Date:  November 6 (Tue), 2007, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Masayasu Moriwaki (森脇政泰) (Hiroshima University) 
Title:  Multiplicityfree decompositions of the minimal representation of the indefinite orthogonal group 
Abstract: [ pdf ] 
A unitary representation of a reductive Lie group can decompose
when restricted to a subgroup which is a symmetric pair
with finite or infinite multiplicity.
On the other hand, T. Kobayashi proved that
an irreducible unitary highest weight representation of scalar type
decomposes with multiplicityfree
when restricted to any subgroup which is a semisimple symmetric pair,
and R. Howe proved that the Weil representation decomposes
with multiplicityfree when restricted to any subgroup which is a dual pair.
In this talk, with respect to the minimal representation of the indefinite orthogonal group which was constructed by Kazhdan, Kostant, BinegarZierau and KobayashiØrsted, we will show that the multiplicityfree theorem holds when restricted to more subgroups than symmetric subgroups. 
Date:  November 20 (Tue), 2007, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Kyo Nishiyama (西山 享) (Kyoto University) 
Title:  Asymptotic cone for semisimple elements and the associated variety of degenerate principal series 
Abstract: [ pdf ] 
Let a be a hyperbolic element in a semisimple Lie algebra over the real number field. Let K be the complexification of a maximal compact subgroup of the corresponding real adjoint group. We study the asymptotic cone of the semisimple orbit through a under the adjoint action by K. The resulting asymptotic cone is the associated variety of a degenerate principal series representation induced from the parabolic associated to a. 
Date:  December 11 (Tue), 2007, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Junko Inoue (井上順子) (Tottori University) 
Title:  Characterization of some smooth vectors for irreducible representations of exponential solvable Lie groups 
Abstract: [ pdf ] 
This is a joint work with Jean Ludwig (University of Metz). Let G be an exponential solvable Lie group, and π be an irreducible unitary representation of G. By induction from a character on a connected subgroup H, π is realized on a Hilbert space of L^{2}functions on a homogeneous space G/H. We investigate a subspace SE of C^{∞}vectors of π consisting of functions with a certain property of rapidly decreasing at infinity. We give a description of SE as the space of C^{∞}vectors of an extension of π to an exponential solvable group containing G. 
Date:  December 18 (Tue), 2007, 16:3018:00 
Place:  Room 126, Graduate School of Mathematical Sciences, the University of Tokyo 
Speaker:  Noriyuki Abe (阿部紀行) (University of Tokyo) 
Title:  On the existence of homomorphisms between principal series of complex semisimple Lie groups 
Abstract: [ pdf ] 
The principal series representations of a semisimple Lie group play an important role in the representation theory. We study the principal series representation of a complex semisimple Lie group and determine when there exists a nonzero homomorphism between the representations. 
© Toshiyuki Kobayashi