Spin Polynomial Functors and Representations of Schur Superalgebras
نویسنده
چکیده
We introduce categories of homogeneous strict polynomial functors, Pold,k and Pol II d,k, defined on vector superspaces over a field k of characteristic not equal 2. These categories are related to polynomial representations of the supergroups GL(m|n) and Q(n). In particular, we prove an equivalence between Pold,k, Pol II d,k and the category of finite dimensional supermodules over the Schur superalgebra S(m|n, d), Q(n, d) respectively provided m,n ≥ d. We also discuss some aspects of Sergeev duality from the viewpoint of the category Pol d,k.
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