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