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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some interesting nonspherical tempered representations of graded Hecke algebras


Author: C. Kriloff
Journal: Trans. Amer. Math. Soc. 351 (1999), 4411-4428
MSC (1991): Primary 16G99
Published electronically: February 10, 1999
MathSciNet review: 1603914
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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.


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Additional Information

C. Kriloff
Affiliation: Department of Mathematics\ Idaho State University\ Pocatello, Idaho 83209-8085
Email: krilcath@isu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02308-9
PII: S 0002-9947(99)02308-9
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
Article copyright: © Copyright 1999 American Mathematical Society