2004/03/31 by Eric C. Rowell
Mathematics · #Algebraic structures and combinatorial models #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.QA #math.RT #msc:18D10 #msc:20F36 #msc:20G42
paper · pdf · doi:10.1007/s00209-005-0773-1
published as Math. Z. vol. 250 no. 4 (2005) 745-774. · 25 pages, 1 figure. Final verstion to appear in Math. Z. Changes: expanded to include Lie type C, clarified/justified use of fusion rule result due to Andersen-Paradowski and to Sawin in the general case (reference added)
arxiv created 2005/03/02 · openalex publication_date 2005/04/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
We consider two families of categories. The first is the family of semisimple quotients of H. Andersen's tilting module categories for quantum groups of Lie type B specialized at odd roots of unity. The second consists of categories constructed from a particular family of finite-dimensional quotients of the group algebra of Artin's braid group known as BMW-algebras of type BC. Our main result is to show that these families coincide as braided tensor categories using a recent theorem of Tuba and Wenzl. The morphism spaces in these categories can be equipped with a Hermitian form, and we are able to show that these categories are never unitary, and no braided tensor category sharing the Grothendieck semiring common to these families is unitarizable.