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A Classification of Spherical Schubert Varieties in the Grassmannian

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Hodges,  Reuven
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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arXiv:1809.08003.pdf
(Preprint), 347KB

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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.