Research Inspiration from Mathematical Sciences Research Institute for Mathematical SciencesKyoto University

## August 12-16, 2001

The Workshop is to be held at Kansai Seminar House where accommodation and meals (according to the program below) for all speakers and most participants will be provided.

time August 12
(Sun)
August 13
(Mon)
August 14
(Tue)
August 15
(Wed)
August 16
(Thu)
8:00 - 9:00 Breakfast Breakfast Breakfast Breakfast
9:30 - 10:30

Miyachi Naito Otofuji Dong
10:45 - 11:45 Braverman Frenkel Semenov-
Tian-Shansky
Zabrocki
12:15 - 13:00 Registration Lunch Lunch Lunch Lunch
13:15 - 14:15 Wakimoto Feigin Discussions Discussions Noumi
14:30 - 15:30 Caldero Discussions Discussions Discussions van Diejen
15:45 - 16:45 Terao Discussions Discussions Discussions Kirillov
17:00 - 18:00 Nakayashiki Discussions Discussions Discussions Discussions
18:00 - 18:45 Dinner Dinner Dinner Dinner Dinner
19:00 - 20:00 Reception Malkin Teleman Jinzenji Bonfire
20:15 - 21:15 Reception Saito Derksen Takahashi Bonfire

### Daily Program

 August 12 Sunday 12:30 - 13:00 Registration 13:15 - 14:15 Minoru Wakimoto (Kyushu University): N=2 superconformal modules with half-modular properties 14:30 - 15:30 Philippe Caldero (University Claude Bernard Lyon I, France): Adapted algebras for the Berenstein-Zelevinsky conjecture 15:45 - 16:45 Hiroaki Terao (Tokyo Metropolitan University): Multiderivations of Coxeter arrangements 17:00 - 18:00 Atsushi Nakayashiki (Kyushu University): On the space of local operators of SU(2) invariant Thirring model 18:00 - 19:00 Dinner 19:00 - 21:00 Reception August 13 Monday 8:00 - 9:00 Breakfast 9:30 - 10:30 Hyohe Miyachi (Science University of Tokyo): On some crystallized decomposition numbers 10:45 - 11:45 Alexander Braverman (Harvard University, USA): Drinfeld's compactifications and periodic Kazhdan-Lusztig polynomials 12:15 - 13:00 Lunch 13:15 - 14:15 Boris Feigin (Landau Inst. for Theoretical Physics, Russia, and RIMS, Kyoto University):to be announced 14:30 - 18:00 Discussions 18:00 - 18:45 Dinner 19:00 - 20:00 Anton Malkin (Yale University, USA): Induction of singular quiver varieties 20:15 - 21:15 Yoshihisa Saito (University of Tokyo): On elliptic Lie algebras August 14 Tuesday 8:00 - 9:00 Breakfast 9:30 - 10:30 Satoshi Naito (University of Tsukuba): Twining characters, Path models, and crystal bases 10:45 - 11:45 Edward Frenkel (University of California at Berkeley, USA): Representations of p-adic and quantum affine groups 12:15 - 13:00 Lunch 13:00 - 18:00 Discussions 18:00 - 18:45 Dinner 19:00 - 20:00 Constantin Teleman (Cambridge University, United Kingdom): The Strong Macdonald conjecture and geometric applications 20:15 - 21:15 Harm Derksen (University of Michigan, Ann Arbor, USA): Quiver representations and Littlewood-Richardson coefficients August 15 Wednesday 8:00 - 9:00 Breakfast 9:30 - 10:30 Takashi Otofuji (Nihon University): Quantum cohomology algebra of infinite-dimensional flag manifolds 10:45 - 11:45 Michael Semenov-Tian-Shansky (University of Bourgogne, France, and Steklov Mathematical Institute, St.Petersburg, Russia): q-deformed quantum Toda lattice: a hint to representation theory of noncompact quantum groups 12:15 - 13:00 Lunch 13:00 - 18:00 Discussions 18:00 - 18:45 Dinner 19:00 - 20:00 Masao Jinzenji (Hokkaido University): Gauss-Manin system and the virtual structure constants 20:15 - 21:15 Atsushi Takahashi (RIMS, Kyoto University): BPS invariants on Calabi-Yau 3-fold August 16 Thursday 8:00 - 9:00 Breakfast 9:30 - 10:30 Chongying Dong (University of California at Santa Cruz, USA): Vertex operator algebras and reductive Lie algebras 10:45 - 11:45 Michael Zabrocki (York University, Canada): q-analogs in Hopf algebra structures 12:15 - 13:00 Lunch 13:15 - 14:15 Masatoshi Noumi (Kobe University): q-Painleve equations arising from a discrete version of the modified KP hierarchy 14:30 - 15:30 Jan Felipe van Diejen (University of Talca, Chile): Modular hypergeometric sums 15:45 - 16:45 Anatol Kirillov (RIMS, Kyoto University, and Steklov Mathematical Institute, St.Petersburg, Russia): Generalized saturation conjecture 16:45 - 18:00 Discussions 18:00 - 19:00 Dinner 19:00 - 22:00 Bonfire

Harm Derksen (University of Michigan, Ann Arbor, USA)
Quiver Representations and Littlewood-Richardson Coefficients
Abstract: I will discuss quiver representations and a theorem about generators of rings of semiinvariants for quivers. Applied to the triple flag quiver, the theorem implies the result of Knutson and Tao about the saturation of Littlewood-Richardson coefficients. Using quiver representations, one can also describe the faces (of arbitrary dimension) of the cone of nonzero Littlewood-Richardson coefficients.

Jan-Felipe van Diejen (University of Talca, Chile)
Modular hypergeometric sums
Abstract:
Recenlty Frenkel and Turaev introduced a modular hypergeometric generalization of the celebrated very-well-poised balanced basic hypergeometric ${}_8\Phi_8$ sum. In this talk various multidimensional generalizations of the Frenkel-Turaev sum are discussed.

Edward Frenkel (University of California at Berkeley, USA)
Representations of p-adic and quantum affine groups
Abstract: It is well-known that the category of unipotent representations of p-adic GL_n over the field of complex numbers is equivalent to the category of finite-dimensional representations of the corresponding affine Hecke algebra, which is in turn equivalent to a subcategory of the category of finite-dimensional representations of the quantum affine algebra of gl(N) for large N, via Jimbo's generalization of the Schur functor (with q=p). Recently, Vigneras has considered unipotent representations of p-adic GL_n over a field of characteristic l>0, prime to p. This category turns out to be related to the category of finite-dimensional representations of quantum affine gl(N), where q is a root of unity of order equal to the order of p mod l. In this talk I will discuss this correspondence, and also review recent results (obtained jointly with E.Mukhin) on the Hopf algebra structure of the Grothendieck ring of finite-dimensional representations of quantum affine gl(N), as N goes to infinity, both when q is generic and a root of unity.