Abstract:
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