q-Centralizer algebras for spin group

Rosa Orellana

Dartmouth College

October 6,
refreshments at 3:45pm


In this talk we describe a centralizer algebra of the quantum group corresponding to the even orthogonal algebras. We use combinatorics of the theory of weights for labeling irreducible representations of Lie algebras and their correspondence to Young diagrams to give a labeling set for the irreducibles of this centralizer algebra.

We will describe the connection of this algebra to q-Brauer algebras and in particular to the type B q-Brauer algebra, which has been defined by Häring under the name B-BMW algebra. Our approach gives combinatorial proofs for the results about the structure of the B-BMW algebra. Moreover, we obtain an explicit formula for the weights of the Markov trace on this algebra. These weights are important in determining exactly when the B-BMW algebra is semisimple.

Joint work with H. Wenzl

Speaker's Contact Info: Rosa.C.Orellana(at-sign)dartmouth.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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