Mathematics – Quantum Algebra
Scientific paper
2004-03-12
Math. Z. vol. 250 no. 4 (2005) 745-774.
Mathematics
Quantum Algebra
25 pages, 1 figure. Final verstion to appear in Math. Z. Changes: expanded to include Lie type C, clarified/justified use of f
Scientific paper
10.1007/s00209-005-0773-1
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.
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