qCentralizer algebras for spin groupRosa OrellanaDartmouth College
October 6,

ABSTRACT


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 qBrauer algebras and in particular to the type B qBrauer algebra, which has been defined by Häring under the name BBMW algebra. Our approach gives combinatorial proofs for the results about the structure of the BBMW 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 BBMW algebra is semisimple. Joint work with H. Wenzl 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

