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Euler–Poincaré Pairings and Elliptic Representations of Weyl Groups and p-Adic Groups

Published online by Cambridge University Press:  04 December 2007

Mark Reeder
Mark Reeder
Affiliation:
Department of Mathematics, Boston College, Chestnut Hill, MA 02467, U.S.A. E-mail: reederma@bc.edu
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Abstract

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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

Keywords

elliptic representationsWeyl groupsp-adic groups
Type
Research Article
Information
Compositio Mathematica , Volume 129 , Issue 2 , November 2001 , pp. 149 - 182
Copyright
© 2001 Kluwer Academic Publishers