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Combinatorics Seminar

q-Whittaker functions, finite fields, and Jordan forms
Friday, September 30, 2022
3:00-4:00 PM
4088 East Hall Map
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.

Speaker(s): Steven Karp (University of Notre Dame)
Building: East Hall
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics