A new quantum analog of the Brauer algebra

Details A new quantum analog of the Brauer algebra A new quantum analog of the Brauer algebra

2002-11-05

arxiv.org/abs/math/0211082v1

Czech. Journal of Physics 53 (2003), 1073-1078.

Mathematics

Quantum Algebra

13 pages

Scientific paper

10.1023/B:CJOP.0000010536.64174.

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.

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