A generating function for the trace of the Iwahori-Hecke algebra

Details A generating function for the trace of the Iwahori-Hecke algebra A generating function for the trace of the Iwahori-Hecke algebra

2000-12-31

arxiv.org/abs/math/0101006v1

Mathematics

Representation Theory

Scientific paper

The Iwahori-Hecke algebra has a ``natural'' trace $\tau$. 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 ${\bf C}[\theta_x]$, that was described and studied by Bernstein, Zelevinski and Lusztig. In this note we compute the generating function for the value of $\tau$ on the basis $\theta_x$.

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