Schur algebras for the alternating group and Koszul duality
نویسندگان
چکیده
منابع مشابه
Schur Algebras and Schur - Weyl Duality
In this paper we study Schur-Weyl duality between the symplectic group and Brauer’s centralizer algebra over an arbitrary infinite field K. We show that the natural homomorphism from the Brauer’s centralizer algebra Bn(−2m) to the endomorphism algebra of tensor space (K) as a module over the symplectic similitude group GSp2m(K) (or equivalently, as a module over the symplectic group Sp2m(K)) is...
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3 Koszul duality 22 3.1 Quadratic algebras . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2 Dual coalgebra and algebra . . . . . . . . . . . . . . . . . . . . . 23 3.3 Some more examples . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.1 The free algebra . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.2 An example from Fröberg . . . . . . . . . . . . . . . . . . 28 3.3.3 ...
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Let g be a reductive Lie algebra over a field of characteristic zero. Suppose that g acts on a complex of vector spaces M by iλ and Lλ, which satisfy the same identities that contraction and Lie derivative do for differential forms. Out of this data one defines the cohomology of the invariants and the equivariant cohomology of M. We establish Koszul duality between them.
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In this paper we prove the Schur-Weyl duality between the symplectic group and the Brauer algebra over an arbitrary infinite field K. We show that the natural homomorphism from the Brauer algebra Bn(−2m) to the endomorphism algebra of the tensor space (K2m)⊗n as a module over the symplectic similitude group GSp2m(K) (or equivalently, as a module over the symplectic group Sp2m(K)) is always surj...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2020
ISSN: 1945-5844,0030-8730
DOI: 10.2140/pjm.2020.306.153