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

2008/10/29 by Dan Ciubotaru, Ciubotaru, Dan
Mathematics · #22E50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:22E50

paper · pdf · doi:10.48550/arxiv.0810.5366

46 pp

arxiv created 2008/10/29 · openalex publication_date 2008/10/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 F₄. 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.

Citations

• Unitary spherical spectrum for split classical groups

Related

• Unitary equivalences for reductive p-adic groups
• Local Langlands Correspondence for Classical Groups and Affine Hecke\n Algebras
• Weyl groups, the Dirac inequality, and isolated unitary unramified representations
• The asymptotic Hecke algebra and rigidity
• Generic unipotent standard modules