## Lie Groups and Representation Theory Seminar at the University of Tokyo 1999

 (Joint seminar of Topology-Lie Groups and Representation Theory) Date: May 11 (Tue), 1999, 16:30-18:00 Speaker: Toshiyuki Kobayashi (яrs) (University of Tokyo) Title: [[}l̂ɂsAQ Abstract: 1) [ Riemann l̂ւ̗UQ̍pŗLsAɂȂ邽߂̔ 2) RpNg Clifford-Klein ̑ݖ 3) [[} RpNg Clifford-Klein̘Aό̈ [ Riemann l̂ɓϊƂčp闣UQ͕KŗLsAɍp ȂB, UQɂ鏤Ԃ͕K Hausdorff ł͂ȂB̎ , ǏIɋ[ Riemann l̂Ɠ^ł悤ȑl̂̊{Qɂ͋ 񂪂邱ƂĂBႦ, ȗ[cl̂̊{Q L^ Calabi-Markus (1962, Ann.Math.) ͂̂PłB(1)ł, ϊQ̌ŗLsA̔𔼒P[Q̍\pďؖB , ŗLsARȍp^ꂽƂ, ̗UQɂ鏤Ԃ Rɑl̂̍\B̑l̂ Clifford-Klein ƌĂԁB Riemann Ώ̋Ԃɂ͏ɃRpNg Clifford-Klein ݂ (Borel)B , [ Riemann Ԃɂ̓RpNg Clifford-Klein ݂ꍇ ݂ȂꍇB͖̔ł邪, \^B Ō, sAQ̕όɂĐGꂽB Riemann Ώ̋Ԃ̃RpNg Clifford-Klein ŘAόł̂, 2,Ȃ킿[}ʂ̏ꍇɌ (Selberg-Weil ̌ÓTIȋǏ藝)B , [ Riemann Ώ̋Ԃł͍łAόłsAQ݂B (1) ̔p,Ǐό̗ʓI]^邱ƂɐGꂽB Date: May 18 (Tue), 1999, 16:30-18:00 Speaker: Itaru Terada (c ) (University of Tokyo) Title: Brauer diagrams, updown tableaux and nilpotent matrices Abstract: Robinson-Schensted Ή̕ώ̈Ƃ, Brauer diagram updown tableau ̊Ԃ̑SP˂^̂B ̍uł͂ɑ΂, Steinberg IWi Robinson-Schensted Ήɑ΂ė^̂Ɠ _Ŋ􉽓Iȉ߂^BSteinberg ̌ʂł, $\Bbb C^n$ ̓ complete flag $F$, $F'$ , $GL( n, \Bbb C )$ ̒ $F$, $F'$ Œ肷镔Q Lie ɑׂs $N$ Ƃ̎Og $( N, F, F' )$ Ŝ̂Ȃ㐔l̂p邪, ɓƂ version ł $\Bbb C^{ 2 n }$ complete flag $F$ Ɠ Ԃ nondegenerate alternating bilinear form $\omega$, $GL( 2 n, \Bbb C )$ ̒ $F$, $\omega$ Œ肷镔Q Lie ɑׂsƂ̎OgݑŜ̂Ȃ㐔l̂pB Date: May 25 (Tue), 1999, 16:30-18:00 Speaker: Toshio Oshima (哇Y) (University of Tokyo) Title: P Lie Q̑މ\Â Abstract: P Lie Q̑މ\ẤA Օ̗CfAɑΉ邪A̐̋̓I\iɂ ̃ACfAjƉpAі̖ɂďqׂB ́ALie ̐\OɑΉAމĂȂꍇ ͍ő原̔POłB̏ꍇ̍̕\Ƃ́A Harish-Chandra ^̋tʑ߂邱Ƃɂ邪Aމꍇ ̈ʉe[}ƂȂB Date: June 1 (Tue), 1999, 16:30-18:00 Speaker: Hisayosi Matumoto ({v) (University of Tokyo) Title: ÓTQ̂މnɂ Abstract: ȖQ̑މn\͂郉NP̕Q Ɏn\̒aɗUIɕꍇB ̂悤ȏꍇɂ͂̕A Ƃ̑މn\̉񐫂݂тBʂȏꍇƂ Johnson ēꂽ̑މn\̊񐬕ւ̂̕肩 ƂłB Date: July 6 (Tue), 1999, 16:30-18:00 Speaker: Weisheng Yang (SUNY-Albany & Sophia University) Title: Two classes of holomorphic function spaces--$Q_p$ and $Q_{p,0}$ Abstract: In this talk, I would like to introduce two classes of holomorphic function spaces in the unit ball of $C^n$--$Q_p$ and $Q_{p,0}$ spaces. We define these classes of function spaces by invariant gradient, invariant Green's function and invariant measure. We proved that $Q_p$ and $Q_{p,0}$ are invariant Banach spaces. We also proved that when $1 < p < \frac{n}{n-1}$, $Q_p$=Bloch space, $Q_{p,0}$=litte Bloch space and $Q_1$=BMOA and $Q_{1,0}$=VMOA. I would like to introduce some other properties of these function. Date: July 13 (Tue), 1999, 16:30-18:00 Speaker: Stephan Mohrdieck (Universität Hamburg & RIMS, Kyoto University) Title: Outer Conjugacy Classes of Non-connected Algebraic Groups with Simple Unit-Component Abstract: In this talk I will give a description of the invariant theory and conjugacy classes of an outer component of a non-connected algebraic group of ADE type, where the unit-component G acts by conjugation. We will work over an algebraically closed field of characteristic 0 and a simply connected unit component, but most of the results will also hold in a more general situation. The outer component is in this case described by an automorphism of the Dynkin diagram of G. The categorial quotient turns out to be equal to the quotient of the fixed point torus of the corresponding automorphism by a semi-direct extension of the fixed point Weyl group, which again is isomorphic to an affine space. The quotient map is a flat morphism with reduced, normal fibres, each consisting of finitely many conjugacy classes. I will also construct a "Steinberg cross-section", i.e. a closed subvariety of the outer component, isomorphic to an affine space, meeting each regular orbit once, on which the restriction of the quotient map is an isomorphism. Date: October 12 (Tue), 1999, 16:30-18:00 Speaker: Nobukazu Shimeno (M) (Okayama University of Science) Title: t[G͂ɂsm萫ɂ Abstract: t[G͂ɂsm萫Ƃ́C֐ ̃t[Gϊ͓ɁgȂȂhƂ咣 ŁCł͓ɁCÓTIȃt[G͂ɂnC[xO ̕sƃn[fB̒藝lDΏ̋ԏ̃t[ Gϊу[gnɕt􉽊֐ɂt[Gϊ iDunkl ϊ Heckman-Opdam ϊjɊg邱Ƃ_ D Date: October 19 (Tue), 1999, 16:30-18:00 Speaker: Andreas Nilsson (University of Tokyo) Title: Spectral multipliers on quotients by amenable subgroups Abstract: In this talk I will present some joint work with Lohoue' concerning spectral multipliers on certain homogeneous spaces. Our interest has been to extend a result by Taylor for Riemannian manifolds to qoutients of semi-simple Lie groups by amenable subgroups. Date: November 9 (Tue), 1999, 16:30-17:30 Speaker: Soren Illman (University of Helsinki) Title: Hilbert's fifth problem and proper actions of Lie groups Abstract: First we discuss Hilbert's fifth problem, concerning Lie's theory of transformation groups, and earlier known results. Then we present the result that every smooth proper action of a Lie group is equivalent to a real analytic action. We also describe a uniqueness result concerning the obtained real analytic structure. Date: November 30 (Tue), 1999, 16:30-17:30 Speaker: Tomoyuki Kakehi ( mV) (Tsukuba University) Title: Pfaffian systems and Radon transforms on affine Grassmann manifolds Abstract: {uł́AAt@COX}l̏ɃptBAƌĂ ̍s񎮌^pf\Ap At@COX}l̏̃hϊ̑ÂB XɁAhϊ̔]ɂĂAptBAp ̓Iȕ\^B A{u̓éATufts w Fulton Gonzalez Ƃ̋ɊÂ ̂łB Date: January 18 (Fri), 2000, 16:30-18:00 Speaker: Yoshiaki Kakiichi (`sǖ) (Toyo University) Title: [㐔yуX[p[[㐔 Date: January 25 (Tue), 2000, 16:30-18:00 Place: Room 122, Graduate School of Mathematical Sciences, Komaba Speaker: Toshihiko Matsuki (ؕqF) (Kyoto University) Title: [Q̋OɌ郏CQ̕Q̐ɂ Abstract: P[Q standard Cartan Q T ̂Q regular element ł邽߂̕Kv\͂炪 W_K(T) ňڂ荇ƂłB W_K(T) ͊l̏̋Oł{IłB搶Ƃ̋c_̒琶܂ W_K(T) ̐ɂĂ̗\zؖł܂̂ŕ񍐂Ǝv܂B Ȁ݂͖ؖ{IȂƂ낪 case-by-case check ł̂słB