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Abstract: 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.
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