Classification of Levi-spherical Schubert varieties

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