### Abstract

Original language | English |
---|---|

Pages (from-to) | 425-435 |

Number of pages | 11 |

Journal | Archiv der Mathematik |

Volume | 93 |

Issue number | 5 |

DOIs | |

Publication status | Published - Nov 2009 |

### Fingerprint

### Keywords

- Schur–Weyl duality

### Cite this

*Archiv der Mathematik*,

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

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

Research output: Contribution to journal › Article

*Archiv der Mathematik*, vol. 93, no. 5, pp. 425-435. https://doi.org/10.1007/s00013-009-0066-8

}

TY - JOUR

T1 - Schur-Weyl duality over finite fields

AU - Benson, David

AU - Doty, Stephen

PY - 2009/11

Y1 - 2009/11

N2 - 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.

AB - 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.

KW - Schur–Weyl duality

U2 - 10.1007/s00013-009-0066-8

DO - 10.1007/s00013-009-0066-8

M3 - Article

VL - 93

SP - 425

EP - 435

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

IS - 5

ER -