Schur functions, quantum affine algebras and a discrete dynamical systemMichael KleberMIT
Joint meeting with the Lie Groups seminar.

ABSTRACT


Consider the finitedimensional irreducible representations of SL(n) whose highest weights are multiples of a fundamental weight  or alternatively, the Schur functions associated to rectangular Young diagrams. They turn out to be a solution to a discrete version of an integrable dynamical system, the ``discrete Hirota relations.'' Surprisingly, if we try to solve the same system for the other classical root systems, the representations that pop out appear to be irreducibles of the associated quantum affine algebra. We will talk about current work to generalize this whole picture to all highest weights, not just rectangles. The first step is a multitime generalization of the discrete Hirota system, and the second step is finding a solution over symplectic or orthogonal representations. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

