Algebraic Combinatorics Seminar - Steven Karp

Thursday, May 20, 2021 1:00 pm - 1:00 pm EDT (GMT -04:00)

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

Speaker: Steven Karp
Affiliation: UQAM
Zoom: Contact Steve Melczer


The q-Whittaker symmetric function associated to an integer partition is a q-analogue of the Schur symmetric function. We give a new formula for the q-Whittaker function in terms of 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). This is joint work with Hugh Thomas.