Item

Abstract

Let $L$ be a Levi subgroup of $GL_N$ which acts by left multiplication on a
Schubert variety $X(w)$ in the Grassmannian $G_{d,N}$. We say that $X(w)$ is a
spherical Schubert variety if $X(w)$ is a spherical variety for the action of
$L$. In earlier work we provide a combinatorial description of the
decomposition of the homogeneous coordinate ring of $X(w)$ into irreducible
$L$-modules for the induced action of $L$. In this work we classify those
decompositions into irreducible $L$-modules that are multiplicity-free. This is
then applied towards giving a complete classification of the spherical Schubert
varieties in the Grassmannian.