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Representation Theory

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ISSN 1088-4165

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Involutions in Weyl groups
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by Robert E. Kottwitz PDF
Represent. Theory 4 (2000), 1-15 Request permission

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