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Representation Theory

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Hecke modules based on involutions in extended Weyl groups

Author: G. Lusztig
Journal: Represent. Theory 22 (2018), 246-277
MSC (2010): Primary 20G99, 33D80
Published electronically: December 20, 2018
MathSciNet review: 3892873
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Abstract: Let $X$ be the group of weights of a maximal torus of a simply connected semisimple group over $\mathbf {C}$ and let $W$ be the Weyl group. The semidirect product $W((\mathbf {Q}\otimes X)/X)$ is called an extended Weyl group. There is a natural $\mathbf {C}(v)$-algebra $\mathbf {H}$ called the extended Hecke algebra with basis indexed by the extended Weyl group which contains the usual Hecke algebra as a subalgebra. We construct an $\mathbf {H}$-module with basis indexed by the involutions in the extended Weyl group. This generalizes a construction of the author and Vogan.

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Additional Information

G. Lusztig
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
MR Author ID: 117100

Received by editor(s): November 8, 2017
Received by editor(s) in revised form: October 5, 2018
Published electronically: December 20, 2018
Additional Notes: This research was supported by NSF grant DMS-1566618.
Article copyright: © Copyright 2018 American Mathematical Society