BMW algebra, quantized coordinate algebra and type C Schur--Weyl duality

Details BMW algebra, quantized coordinate algebra and type C Schur--Weyl duality BMW algebra, quantized coordinate algebra and type C Schur--Weyl duality

2007-08-22

arxiv.org/abs/0708.3009v3

Mathematics

Quantum Algebra

to appear in Representation Theory, an electronic journal of the AMS

Scientific paper

We prove an integral version of the Schur--Weyl duality between the specialized Birman--Murakami--Wenzl algebra $B_n(-q^{2m+1},q)$ and the quantum algebra associated to the symplectic Lie algebra sp_{2m}. In particular, we deduce that this Schur--Weyl duality holds over arbitrary (commutative) ground rings, which answers a question of Lehrer and Zhang [Strongly multiplicity free modules for Lie algebras and quantum groups, J. Algebra (1) 306 (2006), 138--174] in the symplectic case. As a byproduct, we show that, as $Z[q,q^{-1}]$-algebra, the quantized coordinate algebra defined by Kashiwara is isomorphic to the quantized coordinate algebra arising from a generalized Faddeev--Reshetikhin--Takhtajan's construction.

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