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Involutions in Weyl groups

Author(s): Robert E. Kottwitz
Journal: Represent. Theory 4 (2000), 1-15.
MSC (2000): Primary 20F55; Secondary 22E50
Posted: February 1, 2000
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Abstract: Let $G$ be a split real group with Weyl group $W$. Let $E$ be an irreducible representation of $W$. Let $V$ be the stable Lie algebra version of the coherent continuation representation of $W$. The main result of this paper is a formula for the multiplicity of $E$ in $V$. The formula involves the position of $E$ in Lusztig's set $\coprod \mathcal M(\mathcal{G})$. The paper treats all quasi-split groups $G$ as well.

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Additional Information:

Robert E. Kottwitz
Affiliation: Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, Illinois 60637
Email: kottwitz@math.uchicago.edu

DOI: 10.1090/S1088-4165-00-00050-9
PII: S 1088-4165(00)00050-9
Received by editor(s): May 14, 1998
Received by editor(s) in revised form: August 25, 1999
Posted: February 1, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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