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Whittaker unitary dual of affine graded Hecke algebras of type E

Part of: Lie groups Representation theory of groups

Published online by Cambridge University Press:  03 December 2009

Dan Barbasch  and
Dan Ciubotaru
Dan Barbasch
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853, USA (email: barbasch@math.cornell.edu)
Dan Ciubotaru
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA (email: ciubo@math.utah.edu)
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Abstract

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This paper gives the classification of the Whittaker unitary dual for affine graded Hecke algebras of type E. By the Iwahori–Matsumoto involution, this is also equivalent to the classification of the spherical unitary dual for type E. Together with some results of Barbasch and Moy (D. Barbasch and A. Moy, Unitary spherical spectrum for p-adic classical groups, Acta Appl. Math. 44 (1996), 3–37; D. Barbasch, The spherical unitary spectrum of split classical real and p-adic groups, Preprint (2006), math/0609828) and Ciubotaru (D. Ciubotaru, The Iwahori spherical unitary dual of the split group of type F4, Represent. Theory 9 (2005), 94–137), this work completes the classification of the Whittaker Iwahori-spherical unitary dual or, equivalently, the spherical unitary dual of any split p-adic group.

Keywords

unitary dualspherical representationssplit p-adic groupsaffine Hecke algebras

MSC classification

Secondary: 22E50: Representations of Lie and linear algebraic groups over local fields 20C08: Hecke algebras and their representations
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 6 , November 2009 , pp. 1563 - 1616
Copyright
Copyright © Foundation Compositio Mathematica 2009

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