# Combinatorics Seminars-Affine evacuation

Speaker: Joel Brewster Lewis, GWU

Date and time: Thursday, October 4, 4–5 pm

Place: Phillips 110

Title: Affine evacuation

Abstract: *Evacuation* (or *Schützenberger's involution*) is an involution on standard Young tableaux of a given shape, closely tied to the combinatorics of permutations via the RSK correspondence. One of its many nice features is that the number of fixed points of shape lambda is equal to the number of domino tableaux of the same shape, and is given by evaluating the natural *q*-analogue of the hook-length formula (counting all tableaux of shape lambda) at *q* = −1.

In this talk, I'll describe a related involution on *tabloids* (which are just like tableaux, but with only the row condition). This involution is related to the combinatorics of the *affine* symmetric group via a generalization of the RSK correspondence. We show that it has many desirable properties; in particular, the number of its fixed points of shape lambda satisfies a domino-like recurrence and is given by an evaluation of a Green polynomial at *q* = −1.

This talk is based on work with Michael Chmutov, Gabriel Frieden, and Dongkwan Kim.