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arXiv · 1804.04702

Representations of monomial matrices and restriction from $GL_n$ to $S_n$

Nate Harman
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Abstract

We outline an approach to understanding restrictions of polynomial representations of $GL_n(\mathbb{C})$ to $S_n$ by first restricting to $T \rtimes S_n$, the subgroup of $n \times n$ monomial matrices. Using this approach we give a combinatorial interpretation for the decomposition of a tensor product of symmetric powers of the defining representation.

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Nate Harman. 2018-04-12. Representations of monomial matrices and restriction from $GL_n$ to $S_n$. https://arxiv.org/abs/1804.04702

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