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On unitary unipotent representations of $p$-adic groups and affine Hecke algebras with unequal parameters
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
doi:10.1090/s1088-4165-08-00338-5
fatcat:pa7sd4xl5vastp3yxeukcj6yna