The space of elliptic virtual representations of a p-adic group is endowed with a natural inner product EP(,), defined analytically by Kazhdan and homologically by Schneider–Stuhler. Arthur has computed EP in terms of analytic R-groups. For Iwahori spherical representations, we show that EP can also be expressed in terms of a corresponding inner product on space of elliptic virtual representations of Weyl groups. This leads to an explicit description of both elliptic representation theories, in terms of the Kazhdan–Lusztig and Springer correspondences
