Brauer algebras, symplectic Schur algebras and Schur-Weyl duality
نویسندگان
چکیده
منابع مشابه
Brauer Algebras, Symplectic Schur Algebras and Schur-weyl Duality
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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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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The representation theory of Hecke algebras has been an important part toward understanding (ordinary or modular) representation theories of finite groups of Lie type. Schur algebras, as endomorphism algebras, connects the representation theory of general linear groups and the representations of symmetric groups via Schur-Weyl duality. The quantum version of Schur-Weyl duality is established by...
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When we were at the beginnings of our careers Sergei’s support helped us to believe in our work. He generously encouraged us to publish our results on Brauer and Birman-Murakami-Wenzl algebras, results which had in part, or possibly in total, been obtained earlier by Sergei himself. He remains a great inspiration for us, both mathematically and in our memory of his kindness, modesty, generosity...
متن کاملDual Partially Harmonic Tensors and Brauer–schur–weyl Duality
We study the Brauer–Schur–Weyl duality between the quotient Bn(−2m)/B (f) n of the Brauer algebra Bn(−2m) and the symplectic group Sp(V ) on the space HT ⊗f n of partially harmonic tensors of valence f in V , where B (f) n is the two-sided ideal generated by e1e3 · · · e2f−1 and 1 ≤ f ≤ [n/2]. We prove that the dimensions of HT ⊗f n and the endomorphism algebra EndKSp(V ) “
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2008
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-07-04179-7