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

 

Classification of one $\textsf{K}$-type representations


Authors: Dan Barbasch and Allen Moy
Journal: Trans. Amer. Math. Soc. 351 (1999), 4245-4261
MSC (1991): Primary 22E50; Secondary 20G05
Published electronically: June 29, 1999
MathSciNet review: 1473430
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Abstract: Suppose $G$ is a simple reductive $p$-adic group with Weyl group $W$. We give a classification of the irreducible representations of $W$ which can be extended to real hermitian representations of the associated graded Hecke algebra $\mathbb{H}$. Such representations correspond to unitary representations of $G$ which have a small spectrum when restricted to an Iwahori subgroup.


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Additional Information

Dan Barbasch
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Email: barbasch@math.cornell.edu

Allen Moy
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: moy@math.loa.umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02171-6
PII: S 0002-9947(99)02171-6
Received by editor(s): July 1, 1996
Received by editor(s) in revised form: June 23, 1997
Published electronically: June 29, 1999
Additional Notes: The authors were supported in part by NSF grants DMS–9401176 and DMS–9500973
Article copyright: © Copyright 1999 American Mathematical Society