石井 基裕（東北大学）「Semi-infinite path model for extremal weight modules over quantum affine algebras」
Extremal weight modules were introduced by M. Kashiwara as natural generalizations of integrable highest weight modules. They are very important to study finite-dimensional representation theory of quantum affine algebras; finite-dimensional representations of quantum affine algebras are studied by many people in connection with integrable systems, geometric, categorical, and combinatorial representation theory. In this talk, I introduce semi-infinite LS paths by using the semi-infinite Bruhat order on affine Weyl groups, and show that they provide an explicit realization of a crystal basis of an extremal weight module. This talk is based on a joint work with S. Naito and D. Sagaki; the preprint is available at "arXiv:1402.3884".