Crystal bases for quantum affine algebras and Young's lego-tetris

Seok-Jin Kang
(Seoul Nat. U./ Yale U.)

In this talk, we will give a combinatorial realization of crystal graphs for basic representations of quantum affine algebras. The crystal bases will be realized as reduced stable Young's legos and the Kashiwara operators will be described in terms of tetris. We will also discuss the connection with the representation theory of Hecke algebras and crystal bases for quantum affine algebras.