A generating function for the trace of the Iwahori-Hecke algebra
Eric M. Opdam
Abstract
The Iwahori-Hecke algebra has a ``natural'' trace τ. This trace is the evaluation at the identity element in the usual interpretation of the Iwahori-Hecke algebra as a sub-algebra of the convolution algebra of a p-adic semi-simple group. The Iwahori-Hecke algebra contains an important commutative sub-algebra C[θx], that was described and studied by Bernstein, Zelevinski and Lusztig. In this note we compute the generating function for the value of τ on the basis θx.
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