Speaker: Jaewon Min (UIUC)
Title: Key polynomials and spherical Schubert varieties
Abstract: A key polynomial, which is also a Demazure character of type A, can be expressed as a summation of products of Schur polynomials. Yibo Gao, Reuven Hodges and Alexander Yong described combinatorially when this expression has multiplicities in order to characterize spherical Schubert varieties. In this talk, we will discuss how to express key polynomials into Schur polynomials using Lakshmibai-Seshadri paths. This is a generalization of Littlewood-Richardson rules for general Lie types and gives another criterion of Schubert varieties being spherical.