@online{2018arXiv180908003H,
TITLE = {A Classification of Spherical Schubert Varieties in the Grassmannian},
AUTHOR = {Hodges, Reuven and Lakshmibai, Venkatramani},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1809.08003},
EPRINT = {1809.08003},
EPRINTTYPE = {arXiv},
YEAR = {2018},
MARGINALMARK = {$\bullet$},
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.},
}