Classification of Levi-spherical Schubert varieties

Abstract

A Schubert variety in the complete flag manifold $G{L}_n/B$ is Levi-spherical if the action of a Borel subgroup in a Levi subgroup of a standard parabolic has a dense orbit. We give a combinatorial classification of these Schubert varieties. This establishes a conjecture of the latter two authors, and a new formulation in terms of standard Coxeter elements. Our proof uses the theory of key polynomials (type A Demazure module characters).

30 pages

References in corpus (3)

• Coxeter combinatorics and spherical Schubert geometry
• Spherical Schubert varieties and pattern avoidance
• Boolean elements in the Bruhat order

Cited by in corpus (1)

• Proper elements of Coxeter groups