Infinite Analysis Seminar Tokyo in 2002
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Residues of q-hypergeometric integrals and
characters of affine Lie algebras
Speaker: Atsushi Nakayashiki (Kyushu Univ.)
Date: 14 December 2002 (Sat), 13:00 -- 14:30.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba
Campus).
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On trigonometric Ruijsenaars-Schneider integrable systems
Speaker: Kazuyuki Oshima (Nagoya Univ.)
Date: 14 December 2002 (Sat), 15:00 -- 16:30.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba Campus).
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Lattice Toda field theory, lattice W algebras and
related topis
Speaker: Rei Inoue (Univ. of Tokyo)
Date: 16 November 2002 (Sat), 13:00 -- 14:00.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba
Campus).
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Spectral curves and parameterizations of a
discrete integrable 3-dimensional model
Speaker: Stanislav Pakuliak
(Joint Institute for Nuclear Research, Russia)
Date: 16 November 2002 (Sat), 14:15 -- 15:15.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba Campus).
Abstract: We consider a discrete classical integrable model on the
3-dimensional cubic lattice. The solutions of this model can be used
to parameterize the Boltzmann weights of the different 3-dimensional
spin models. We have found the general solution of this model
constructed in terms of the theta-functions defined on an arbitrary
compact algebraic curve. The imposing of the periodic boundary
conditions fixes the algebraic curve. We have shown that in this case
the curve coincides with the spectral one of the auxiliary linear
problem. In the case when the curve is a rational one, the soliton
solutions have been constructed.
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Bootstrap equations and XYZ correlation functions
Speaker: Yasuhiro Quano (Suzuka University of Medical Science)
Date: 16 November 2002 (Sat), 15:30 -- 16:30.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba Campus).
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Calculation of Free energy with respect to XXX spin
1/2 chain independent of Quantum Transfer Matrix
method and Thermodynamical Bethe Ansatz method
Speaker: Go Kato (Univ. of Tokyo)
Date: 13 July 2002 (Sat), 14:00 -- 15:00.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba
Campus).
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Degeneration of eigenvalues of the XYZ model and
sl_2 loop algebra
Speaker: Tetsuo Deguchi (Ochanomizu Univ.)
Date: 13 July 2002 (Sat), 15:30 -- 16:30.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba Campus).
Abstract:
A spin chain defined on a finite lattice might have an
infinite dimensional symmetry, and the degree of the
degeneracy might increase exponentially with repect to the
lattice size.
In fact, it is shown in Ref. [1] that if
the anisotropic parameter \Delta =(q+1/q)/2 is given by a
root of unity, q, then it is the case: the (inhomogeneous)
transfer matrix of the the XXZ spin chain under the
P.B.C.s (anti-)commutes with the sl_2 loop algebra. Here,
we have assumed that q^{2N}=1 and q \ne 1, and the lattice
size L is arbitrary. Furthermore, we can show that the
dimension of some degenerate eigenspace is given by
2^{L/N}, if L/N is an even integer. In this talk, we
discuss a generalization of the six-vertex (XXZ) result to
the eight-vertex model (i.e., the XYZ spin chain), where
some degenerate eigenvectors were constructed first by
R.J. Baxter in 1972. We derive a dimension formula for
the XYZ degeneracy, almost rigorously. We also discuss
some physical consequences of the XYZ degeneracy.
[1] T. Deguchi, K. Fabricius and B.M. McCoy,
The sl_2 loop algebra symmetry of the six-vertex model at roots of unity,
J. Stat. Phys. 102 (2001) 701-736.
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Crystal base and quiver variety
Speaker: Yoshihisa Saito (Univ. of Tokyo)
Date: 15 June 2002 (Sat), 14:00 -- 15:00.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba
Campus).
Abstract:
We give a crystal structre on the set of all irreducible components of
Lagrangian subvarieties of quiver varieties. As a crystal, it is
isomorphic to the crystal base of an irreducible highest weight
representation of a quantized universal enveloping algebra.
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On fusion product of finite dimensional modules and conformal
coinvariants
Speaker: Michio Jimbo (Univ. of Tokyo)
Date: 15 June 2002 (Sat), 15:30 -- 16:30.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba Campus).
Abstract:
The behavior of conformal blocks when the insertion poitns
all collide has been a subject of intensive study (Feigin et
al.), though the present knowledge is rather limited. We
discuss here an equivalence between coinvariant spaces of
highest weight modules and those of tensor products of
finite dimensional modules. Using the latter description,
we compute in the sl_2 case the Hilbert polynomials of
coinvariant spaces, in terms of level-restricted Kostka
polynomials. This talk is based on a joint work with
B.Feigin, S.Loktev, R.Kedem and T.Miwa.
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Spin models around the Haldane system and its extension to
electron systems
Speaker: Masanori Yamanaka (Nihon Univ.)
Date: 18 May 2002 (Sat), 14:00 -- 15:00.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba Campus).
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On fusion of the vertex operators in RSOS models
Speaker: Yaroslav Pugai (Univ. of Tokyo)
Date: 18 May 2002 (Sat), 15:30 -- 16:30.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba Campus).
Abstract: The exact description of vertex operators appearing in the
algebraic approach to the two dimensional integrable models of
statistical mechanics leads to the integral representation for
correlation functions / form-factors of these models. Our aim is to
discuss the role of the fusion in this approach. We show that fused
vertex operators carry important information on the vacuum expectation
values of the (properly normalized) local operators in the scaling limit.
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Correlation functions of the XXZ model and combinatorics
Speaker: Nikolai Kitanie (Tokyo Univ.)
Date: 20 Apr. 2002 (Sat), 14:00 -- 15:00.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba Campus).
Abstract: In this talk I give a brief description of a method of
calculation of the correlation functions of the XXZ model, based on the
algebraic Bethe ansatz. Using this method for a special case of the XXZ
model with $\Delta=1/2$ one can calculate some correlation functions,
such as emptiness formation probability, explicitely. It can be shown
that this function can be expressed in terms of the corresponding
number of alternating sign matrices.
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Noncommutative solitons and integrable systems
Speaker: Masashi Hamanaka (Tokyo Univ.)
Date: 20 Apr. 2002 (Sat), 15:30 -- 16:30.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba Campus).
For references and some of his papers, for example,
"Exact BPS solitons in noncommutative gauge theories"
"Recent developments in non-commutative gauge theories"
are available here.
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Generalized supersymmetry and
quasi-exactly solvable quantum mechanical systems
Speaker: Ryu Sasaki (Yukawa Institute, Kyoto University)
Date: 13 February 2002 (Wed), 13:30 -- 14:30.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba Campus).
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Smirnov-type integral for the bulk/boundary XXZ model
in the anti-ferromagnetic regime.
Speaker: Yasuhiro Quano (Suzuka University of Medical Science)
Date: 12 January 2002 (Sat), 13:00 -- 14:00.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba Campus).
Abstract: Presented are the integral solutions to the quantum
Knizhnik-Zamolodchikov equations for the correlation functions
of both the bulk and boundary XXZ models in the anti-ferromagnetic
regime. The difference equations can be derived from Smirnov-type
master equations for correlation functions on the basis of the CTM
bootstrap. Our integral solutions with an appropriate choice of the
integral kernel reproduce the formulae previously obtained by using
the bosonization of the vertex operators of the quantum affine algebra
U_q (\hat sl_2).
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Quasi-exact-solvability of quantum Inozemtsev system
Speaker: Kanehisa Takasaki (Kyoto University)
Date: 12 January 2002 (Sat), 14:30 -- 15:30.
Place: room 117,
Graduate School of Mathematical Sciences,
University of Tokyo (Komaba Campus).