The Birman-Wenzl-Murakami algebra, Hecke algebra and representations of U_{q}(osp(1|2n))

Details The Birman-Wenzl-Murakami algebra, Hecke algebra and representations of U_{q}(osp(1|2n)) The Birman-Wenzl-Murakami algebra, Hecke algebra and representations of U_{q}(osp(1|2n))

2006-07-03

arxiv.org/abs/math/0607049v1

Mathematics

Quantum Algebra

46 pages, 5 figures, essentially the first part of my PhD thesis together with some further work

Scientific paper

A representation of the Birman-Wenzl-Murakami algebra BW_{t}(-q^{2n},q) exists in the centraliser algebra End_{U_q(osp(1|2n))}(V^{\otimes t}), where V is the fundamental (2n+1)-dimensional irreducible U_{q}(osp(1|2n))-module. This representation is defined using permuted R-matrices acting on V^{\otimes t}. A complete set of projections onto and intertwiners between irreducible U_{q}(osp(1|2n))-summands of V^{\otimes t} exists via this representation, proving that End_{U_q(osp(1|2n))}V^{\otimes t}) is generated by the set of permuting R-matrices acting on V^{\otimes t}. We also show that a representation of the the Iwahori-Hecke algebra H_{t}(-q) of type A_{t-1} exists in the centraliser algebra End_{U_q(osp(1|2))}[(V^{+}_{1/2})^{\otimes t}], where V^{+}_{1/2} is a two-dimensional irreducible representation of U_{q}(osp(1|2)).

Affiliated with

Also associated with

No associations

Rating

The Birman-Wenzl-Murakami algebra, Hecke algebra and representations of U_{q}(osp(1|2n)) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Birman-Wenzl-Murakami algebra, Hecke algebra and representations of U_{q}(osp(1|2n)), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Birman-Wenzl-Murakami algebra, Hecke algebra and representations of U_{q}(osp(1|2n)) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-416207