Involutions in Weyl groups

Kottwitz, Robert

doi:10.1090/S1088-4165-00-00050-9

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.

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