2006/07/03 by Sacha C. Blumen, Blumen, Sacha C.
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.QA #math.RT #msc:16G99 #msc:17B37
paper · pdf · doi:10.48550/arxiv.math/0607049
46 pages, 5 figures, essentially the first part of my PhD thesis together with some further work
arxiv created 2006/07/03 · arxiv updated 2009/12/01
A representation of the Birman-Wenzl-Murakami algebra BWt(-q2n,q) exists in the centraliser algebra EndUq(osp(1|2n))(V⊗ t), where V is the fundamental (2n+1)-dimensional irreducible Uq(osp(1|2n))-module. This representation is defined using permuted R-matrices acting on V⊗ t. A complete set of projections onto and intertwiners between irreducible Uq(osp(1|2n))-summands of V⊗ t exists via this representation, proving that EndUq(osp(1|2n))V⊗ t) is generated by the set of permuting R-matrices acting on V⊗ t. We also show that a representation of the the Iwahori-Hecke algebra Ht(-q) of type At-1 exists in the centraliser algebra EndUq(osp(1|2))[(V+1/2)⊗ t], where V+1/2 is a two-dimensional irreducible representation of Uq(osp(1|2)).