Journal of Combinatorics

Volume 7 (2016)

Number 4

A note on the $k\textrm{th}$ tensor product of the defining representation

Pages: 715 – 724

DOI: http://dx.doi.org/10.4310/JOC.2016.v7.n4.a7

Authors

Anthony Mendes (Department of Mathematics, California Polytechnic State University, San Luis Obispo, Calif., U.S.A.)

Marino Romero (Department of Mathematics, University of California at San Diego)

Abstract

Let $D$ be the defining representation of the symmetric group $S_n$. We prove an identity which decomposes the tensor product of $D$ with itself $k$ times into irreducible components using a sign reversing involution.

Keywords

permutation matrices, tensor products, representations of the symmetric group

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Published 16 August 2016