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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
DOI: https://doi.org/10.1090/ert/520
Published electronically: December 20, 2018
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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
Email: gyuri@mit.edu

DOI: https://doi.org/10.1090/ert/520
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

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