## Involutions in Weyl groups

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- by Robert E. Kottwitz
- Represent. Theory
**4**(2000), 1-15 - DOI: https://doi.org/10.1090/S1088-4165-00-00050-9
- Published electronically: 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.## References

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## Bibliographic 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