Schur functions, quantum affine algebras and a discrete dynamical system

Michael Kleber


Joint meeting with the Lie Groups seminar.
NOTE the unusual place and time:

May 10,


Consider the finite-dimensional 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 multi-time generalization of the discrete Hirota system, and the second step is finding a solution over symplectic or orthogonal representations.

Speaker's Contact Info: kleber(at-sign)

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