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Representation Theory
Representation Theory
ISSN 1088-4165

 

On unitary unipotent representations of $ p$-adic groups and affine Hecke algebras with unequal parameters


Author: Dan Ciubotaru
Journal: Represent. Theory 12 (2008), 453-498
MSC (2000): Primary 22E50
Published electronically: December 15, 2008
MathSciNet review: 2465803
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Abstract: We determine the unitary dual of the geometric graded Hecke algebras with unequal parameters which appear in Lusztig's classification of unipotent representations for exceptional $ p$-adic groups. The largest such algebra is of type $ F_4.$ Via the Barbasch-Moy correspondence of unitarity applied to this setting, this is equivalent to the identification of the corresponding unitary unipotent representations with real central character of the $ p$-adic groups. In order for this correspondence to be applicable here, we show (following Lusztig's geometric classification, and Barbasch and Moy's original argument) that the set of tempered modules with real central character for a geometric graded Hecke algebra is linearly independent when restricted to the Weyl group.


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Additional Information

Dan Ciubotaru
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email: ciubo@math.utah.edu

DOI: http://dx.doi.org/10.1090/S1088-4165-08-00338-5
PII: S 1088-4165(08)00338-5
Received by editor(s): January 31, 2007
Published electronically: December 15, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.