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Abstract: In this talk we discuss a method to obtain finite dimensional representations of
the braid group of type B via centralizer algebras of quantum groups. Through this method, for example, we
obtain specializations of the Hecke algebra of type B, Ariki-Koike algebras (also known as cyclotomic Hecke
algebras) and the q-Brauer algebra of type B (also known as the B-BMW algebra). These algebras will be defined
in this talk.
One application of using the method, described in this talk, is that it allows us to define a trace on
these algebras, called the Markov trace. This trace is important in determining when the algebras in the
previous paragraph are semisimple, and also in finding knot/link invariants.
Part of this talk is based on joint work with H. Wenzl.
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