BMW ALGEBRA, QUANTIZED COORDINATE ALGEBRA AND TYPE C SCHUR-WEYL DUALITY

作者：Hu Jun^*

来源：Representation Theory - An Electronic Journal of the AMS, 2011, 15: 1-62.

DOI：10.1090/S1088-4165-2011-00369-1

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 in the symplectic case. As a byproduct, we show that, as a Z[q, q(-1)]-algebra, the quantized coordinate algebra defined by Kashiwara (which he denoted by A(q)(Z)(g)) is isomorphic to the quantized coordinate algebra arising from a generalized Faddeev-Reshetikhin-Takhtajan construction.

• 出版日期2011