8 M ay 2 00 8 SCHUR – WEYL DUALITY OVER FINITE FIELDS
نویسنده
چکیده
We prove a version of Schur–Weyl duality over finite fields. We prove that for any field k, if k has more than r elements, then Schur– Weyl duality holds for the rth tensor power of a finite dimensional vector space V . Moreover, if dimV is at least r + 1 then the natural map kSr → EndGL(V )(V ) is an isomorphism; this isomorphism may fail if dimk(V ) is not strictly larger than r.
منابع مشابه
ar X iv : 0 80 5 . 12 35 v 2 [ m at h . G R ] 3 0 Ju n 20 09 SCHUR – WEYL DUALITY OVER FINITE FIELDS
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 kSr → EndGL(V )(V ) is an isomorphism. This isomorphism may fail if dimk V is not strictly larger than r.
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