Algebraic Combinatorics Seminar - Reuven Hodges

Thursday, October 22, 2020 1:00 pm - 1:00 pm EDT (GMT -04:00)

Title: Coxeter combinatorics and spherical Schubert geometry

Speaker: Reuven Hodges
Affiliation: University of Illinois
Zoom: Contact Karen Yeats


This talk will introduce spherical elements in a finite Coxeter system. These spherical elements are a generalization of Coxeter elements, that conjecturally, for Weyl groups, index Schubert varieties in the flag variety G/B that are spherical for the action of a Levi subgroup. We will see that this conjecture extends and unifies previous sphericality results for Schubert varieties in G/B due to P. Karuppuchamy, J. Stembridge, P. Magyar–J. Weyman-A. Zelevinsky. In type A, the combinatorics of Demazure modules and their key polynomials, multiplicity freeness, and split-symmetry in algebraic combinatorics are employed to prove this conjecture for several classes of Schubert varieties. This talk is based on joint work with Alexander Yong.