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

Dan Ciubotaru
2008 Representation Theory: An Electronic Journal of the AMS  
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
more » ... pondence 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.
doi:10.1090/s1088-4165-08-00338-5 fatcat:pa7sd4xl5vastp3yxeukcj6yna