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q-Whittaker functions, finite fields, and Jordan forms

Steven Karp, LaCIM, Université du Québec à Montréal
Wednesday, April 27, 2022 - 3:30pm to 5:00pm
Online only via Zoom Link:
Steven Karp
Steven Karp


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 \to 0\$ limit, we recover a known description of the classical Burge correspondence (also called column RSK). This is joint work with Hugh Thomas.

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10. These will both be online only.

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Meeting ID: 915 4733 5974