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Paper

#### A Classification of Spherical Schubert Varieties in the Grassmannian

##### Fulltext (public)

arXiv:1809.08003.pdf

(Preprint), 347KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Hodges, R., & Lakshmibai, V. (2018). A Classification of Spherical Schubert Varieties in the Grassmannian. Retrieved from http://arxiv.org/abs/1809.08003.

Cite as: http://hdl.handle.net/21.11116/0000-0002-F4AA-B

##### 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.