Journal article

Characters of algebras containing a Jones basic construction: The Temperley-Lieb, Okada, Brauer, and Birman-Wenzl algebras

T Halverson, A Ram

ADVANCES IN MATHEMATICS | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 1995

Abstract

We begin by determining, in a general form, the characters of irreducible representations of a Jones basic construction and use this result to compute the characters of the Temperley-Lieb algebras and the Okada algebras. In the case of the Birman-Wenzl algebra some of the characters are determined by the general theorem and the others are computed by using the duality between the Birman-Wenzl algebras and the Drinfeld-Jimbo quantum groups of types B and C. The computations involve certain characters of the quantum group; these are polynomials invariant under the Weyl group of type B. We are able to decompose these Weyl group symmetric functions and obtain a combinatorial rule for computing t..

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