### 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 language | English |
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Pages (from-to) | 425-435 |

Number of pages | 11 |

Journal | Archiv der Mathematik |

Volume | 93 |

Issue number | 5 |

DOIs | |

Publication status | Published - Nov 2009 |

### Keywords

- Schur–Weyl duality

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## Cite this

Benson, D., & Doty, S. (2009). Schur-Weyl duality over finite fields.

*Archiv der Mathematik*,*93*(5), 425-435. https://doi.org/10.1007/s00013-009-0066-8