A new quantum analog of the Brauer algebra
arXiv:math/0211082 · doi:10.1023/B:CJOP.0000010536.64174.8e
Abstract
We introduce a new algebra B_l(z,q) depending on two nonzero complex parameters such that B_l(q^n,q) at q=1 coincides with the Brauer algebra B_l(n). We establish an analog of the Brauer-Schur-Weyl duality where the action of the new algebra commutes with the representation of the twisted deformation U'_q(o_n) of the enveloping algebra U(o_n) in the tensor power of the vector representation.
13 pages