Euler-Poincare pairings and elliptic representations of Weyl groups and p-adic groups


We calculate the trace of the Euler-Poincare functions of Iwahori spherical representations. This leads to a classification of elliptic Iwahori-spherical representations in terms of the Langlands parameters assigned to them by Kazhdan and Lusztig. It also gives an explicit and uniform description of the elliptic representation theory of Weyl groups, in terms of the Springer correspondence.