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Cristian Lenart, SUNY Albany – Geometric Methods in Representation Theory Seminar

February 11 @ 4:00 pm - 5:00 pm

Mode: Zoom only

Title: A combinatorial Chevalley formula for semi-infinite flag manifolds and related topics

Abstract: I present a combinatorial Chevalley formula for an arbitrary weight in the equivariant K-theory of semi-infinite flag manifolds, which are certain affine versions of finite flag manifolds G/B. The formula is expressed in terms of the so-called quantum alcove model. One application is a Chevalley formula in the equivariant quantum K-theory of G/B. Another application is that the so-called quantum Grothendieck polynomials represent Schubert classes in the (non-equivariant) quantum K-theory of the type A flag manifold. Both applications solve longstanding conjectures. Other results include the Chevalley formula for partial flag manifolds G/P and related combinatorics of the quantum alcove model. This is joint work with Takafumi Kouno, Satoshi Naito, and Daisuke Sagaki. The talk will be largely self-contained.

Details

Date:
February 11
Time:
4:00 pm - 5:00 pm
Event Category:

Venue

Zoom