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Involutions in Weyl groups


Author: Robert E. Kottwitz
Journal: Represent. Theory 4 (2000), 1-15
MSC (2000): Primary 20F55; Secondary 22E50
DOI: https://doi.org/10.1090/S1088-4165-00-00050-9
Published electronically: February 1, 2000
MathSciNet review: 1740177
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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: https://doi.org/10.1090/S1088-4165-00-00050-9
Received by editor(s): May 14, 1998
Received by editor(s) in revised form: August 25, 1999
Published electronically: February 1, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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