Combinatorics Seminar: A root-system uniform classification of Levi spherical Schubert varieties

Abstract: The study of group orbits and their closures inside flag varieties has a long and storied history. The development of this topic touches on, and interweaves, fundamental ideas from Lie theory, algebraic geometry, representation theory, and algebraic combinatorics. The foundational objects of study in this area are the orbits of Borel subgroups and their closures, the Schubert varieties.

In this talk we will study when a Schubert variety is a spherical variety under the action of certain reductive groups. Spherical varieties generalize several important classes of algebraic varieties including toric varieties, projective rational homogeneous spaces and symmetric varieties.

I will present a root-system uniform, combinatorial classification of Levi-spherical Schubert varieties for any generalized flag variety G/B of finite Lie type. This will be applied to the study of multiplicity-free decompositions of a Demazure module into irreducible representations of a Levi subgroup. I will also discuss recent progress on generalizing the aforementioned results.

Host: Martha Precup