A note on symmetry classes of tensors and Specht modules

Fátima Rodrigues, J.A. Dias da Silva, Pedro C. Silva, Maria M. Torres

Research output: Contribution to journalArticle

Abstract

We construct induced bases for critical orbital spaces indexed by standard tableaux. As a corollary we obtain an explicit isomorphism of C[S-m]-modules between Specht modules and critical orbital spaces which yields a realization of the complete set of complex irreducible representations of the symmetric group in terms of decomposable symmetrized tensors.
Original languageEnglish
Pages (from-to)118-128
Number of pages11
JournalLinear Algebra and Its Applications
Volume531
DOIs
Publication statusPublished - 15 Oct 2017

Keywords

  • Young tableau
  • Specht module
  • Symmetry class of tensors
  • Basic decomposable tensor
  • Orbital space

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