Schur-Weyl duality over finite fields

David Benson, Stephen Doty

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We prove a version of Schur-Weyl duality over finite fields. We prove that for any field k, if k has at least r+1 elements, then Schur-Weyl duality holds for the rth tensor power of a finite dimensional vector space V. Moreover, if the dimension of V is at least r+1, the natural map kSymr to EndGL(V)(V^otimes r) is an isomorphism. This isomorphism may fail if dimk V is not strictly larger than r.
Original languageEnglish
Pages (from-to)425-435
Number of pages11
JournalArchiv der Mathematik
Volume93
Issue number5
DOIs
Publication statusPublished - Nov 2009

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Galois field
Isomorphism
Duality
Vector space
Strictly
Tensor

Keywords

  • Schur–Weyl duality

Cite this

Schur-Weyl duality over finite fields. / Benson, David; Doty, Stephen.

In: Archiv der Mathematik, Vol. 93, No. 5, 11.2009, p. 425-435.

Research output: Contribution to journalArticle

Benson, David ; Doty, Stephen. / Schur-Weyl duality over finite fields. In: Archiv der Mathematik. 2009 ; Vol. 93, No. 5. pp. 425-435.
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