## Some interesting nonspherical tempered representations of graded Hecke algebras

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**351**(1999), 4411-4428 Request permission

## Abstract:

Lusztig’s presentation of the graded Hecke algebra in terms of generators and relations allows for the definition of algebras associated to noncrystallographic root systems. The representation theory of general graded Hecke algebras is investigated, the expected number of tempered representations for $\mathbb {H}(H_3)$ are accounted for, and it is shown that one of these representations has the unexpected property of being nonspherical despite being the only tempered representation appearing at its infinitesimal character. Additional nonspherical tempered representations of $\mathbb {H}(H_4)$ are also included.## References

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## Additional Information

**C. Kriloff**- Affiliation: Department of Mathematics Idaho State University Pocatello, Idaho 83209-8085
- MR Author ID: 630044
- ORCID: 0000-0003-2863-6724
- Email: krilcath@isu.edu
- Received by editor(s): December 1, 1997
- Published electronically: February 10, 1999
- Additional Notes: Supported by an NSF Graduate Research Fellowship and an Alfred P. Sloan Doctoral Dissertation Fellowship
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**351**(1999), 4411-4428 - MSC (1991): Primary 16G99
- DOI: https://doi.org/10.1090/S0002-9947-99-02308-9
- MathSciNet review: 1603914