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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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On unitary unipotent representations of $p$-adic groups and affine Hecke algebras with unequal parameters
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by Dan Ciubotaru PDF
Represent. Theory 12 (2008), 453-498 Request permission


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
  • MR Author ID: 754534
  • Email:
  • Received by editor(s): January 31, 2007
  • Published electronically: December 15, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 12 (2008), 453-498
  • MSC (2000): Primary 22E50
  • DOI:
  • MathSciNet review: 2465803