Date: 03/25/2022

Speaker: Reuven Hodges

Classifying Levi-Spherical Schuber Varieties
A Schubert variety in the complete flag variety $GL_n/B$ is Levi-spherical if the action of a Borel subgroup in a Levi subgroup of a standard parabolic subgroup has an open dense orbit. I will present some recent work, joint with Alexander Yong and Yibo Gao, giving a classification of Levi-spherical Schubert varieties in terms of spherical elements of a symmetric group. As part of this we will discuss the combinatorics of Demazure modules and their key polynomials. I will also discuss a conjectural extension of the classification to other Lie types.