Markov Traces and Generic Degrees in Type Bn

Motivated by the theory of knots, Geck and Lambropoulou studied so-called Markov traces on the Iwahori–Hecke algebra Hn of type Bn. These traces depend on two parameters and are linear combinations of the irreducible characters of Hn, where the coefficients are called weights. Orellana determined the weights explicitly for certain special choices of the parameters. In this article, we derive from Orellanaʹs result a formula for the weights in general. As an application, we obtain a new proof of Hoefsmitʹs formulas for the generic degrees of Hn. Finally, we present a conjectural formula for weights of Markov traces on Ariki–Koike algebras.