Abstract
The main object of this paper is the study of a sequence of finite dimensional algebras, depending on 2 parameters, which appear in connection with the Kauffman link invariant and with Drinfeld's and Jimbo'sq deformation of Lie algebras of typesB, C andD. We determine for which parameters these algebras are semisimple. Moreover, we classify all unitary representations of the infinite braid groupB ∞ factoring through the inductive limit of these algebras. This yields new examples of irreducible subfactors of finite depth, whose indices are squares ofq dimensions of irreducible representations of sympletic and orthogonal groups. In the combinatorial description of these subfactors one naturally obtains truncated Weyl chambers (as for loop groups for a given level) and multiplicity coefficients of fusion rules for Wess-Zumino-Witten models.
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