Adjoint Representations of the Symmetric Group

Mahir Bilen Can; Miles Jones

Adjoint Representations of the Symmetric Group

Representation Theory 2018-04-02 v1 Combinatorics

Authors: Mahir Bilen Can , Miles Jones

Abstract

We study the restriction to the symmetric group, $\mc{S}_n$ of the adjoint representation of $\mt{GL}_n(\C)$ . We determine the irreducible constituents of the space of symmetric as well as the space of skew-symmetric $n\times n$ matrices as $\mc{S}_n$ -modules.

Keywords

adjoint representation symmetric group general linear group irreducible constituents symmetric matrices skew-symmetric matrices module restriction

Cite

@article{arxiv.1803.11473,
  title  = {Adjoint Representations of the Symmetric Group},
  author = {Mahir Bilen Can and Miles Jones},
  journal= {arXiv preprint arXiv:1803.11473},
  year   = {2018}
}

Comments

arXiv admin note: text overlap with arXiv:1708.02995

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