Speaker: Steven Karp, Notre Dame

Title: q-Whittaker functions, finite fields, and Jordan forms

Abstract:

The q-Whittaker symmetric function associated to an integer partition is a q-analogue of the Schur symmetric function. Its coefficients in the monomial basis enumerate partial flags compatible with a nilpotent endomorphism over the finite field of size 1/q. We show that considering pairs of partial flags and taking Jordan forms leads to a probabilistic bijection between nonnegative-integer matrices and pairs of semistandard tableaux of the same shape, which we call the q-Burge correspondence. In the q -> 0 limit, we recover a known description of the classical Burge correspondence (also called column RSK). We use the q-Burge correspondence to prove enumerative formulas for certain modules over the preprojective algebra of a path quiver.

This is joint work with Hugh Thomas.