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 ...

The Donald–Flanigan problem for a finite group H and coefficient ring k asks for a deformation of the group algebra kH to a separable algebra. It is solved here for dihedral groups and Weyl groups of types Bn and Dn (whose rational group algebras are computed), leaving but six finite reflection groups with solutions unknown. We determine the struct...

We prove relations in the braid group that generalize the relations of the formaba=bab. These relations are obtained by means of the generalization to the higher Bruhat orders of the well-known relation between the decompositions of the element of maximal length in the Weyl groupAn−1 and some specific linear orders on the system of positive roots o...

Letp be an odd prime and\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{F}_p $$ \end{document} the finite field withp elements. In the present paper we shall i...