Bmw Algebra, Quantized Coordinate Algebra and Type C Schur–weyl Duality
نویسنده
چکیده
We prove an integral version of the Schur–Weyl duality between the specialized Birman–Murakami–Wenzl algebra Bn(−q , q) and the quantum algebra associated to the symplectic Lie algebra sp2m. In particular, we deduce that this Schur–Weyl duality holds over arbitrary (commutative) ground rings, which answers a question of Lehrer and Zhang ([37]) in the symplectic case. As a byproduct, we show that, as a Z[q, q]-algebra, the quantized coordinate algebra defined by Kashiwara in [33] (which was denoted by Aq(g) there) is isomorphic to the quantized coordinate algebra arising from a generalized Faddeev– Reshetikhin–Takhtajan’s construction (see [23], [28], [46]).
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