# Seminars & Colloquia Calendar

## 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.

Meeting ID: 939 2146 5287

Passcode: 196884, the dimension of the weight 2 homogeneous

subspace of the moonshine module

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