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Lie Group Quantum Mathematics Seminar

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

Cristian Lenart, SUNY Albany

Location:  zoom
Date & time: Friday, 08 October 2021 at 11:00AM - 12:00PM

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 G/B. 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.

Zoom link
Meeting ID: 939 2146 5287
Passcode: 196884, the dimension of the weight 2 homogeneous
subspace of the moonshine module

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