Representations of monomial matrices and restriction from $G{L}_n$ to $S_n$

Abstract

We outline an approach to understanding restrictions of polynomial representations of $G{L}_n(\mathbb{C})$ to $S_n$ by first restricting to $T⋊S_n$, 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.

24 pages

Cited by in corpus (3)

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