Representations of monomial matrices and restriction from GL_n to S_n

2018/04/12 by Nate Harman, Harman, Nate
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1804.04702

openalex publication_date 2018/04/12 · openalex created_date 2018/04/24 · openalex updated_date 2026/07/28

Abstract

We outline an approach to understanding restrictions of polynomial representations of GL_n(ℂ) to S_n by first restricting to T \rtimes S_n, the subgroup of n × 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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