## Hecke modules based on involutions in extended Weyl groups

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**22**(2018), 246-277 Request permission

## 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.## References

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## Additional Information

**G. Lusztig**- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 117100
- Email: gyuri@mit.edu
- 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.
- © Copyright 2018 American Mathematical Society
- Journal: Represent. Theory
**22**(2018), 246-277 - MSC (2010): Primary 20G99, 33D80
- DOI: https://doi.org/10.1090/ert/520
- MathSciNet review: 3892873