Whittaker unitary dual of affine graded Hecke algebras of type E

TL;DR

This paper classifies the Whittaker and spherical unitary duals of affine graded Hecke algebras of type E, completing the classification for split linear algebraic p-adic groups.

Contribution

It provides the first complete classification of the Whittaker unitary dual for affine graded Hecke algebras of type E, linking it to p-adic group representations.

Findings

Classification of the Whittaker unitary dual for type E

Equivalence to spherical unitary dual via Iwahori-Matsumoto involution

Completes the classification for split p-adic groups

Abstract

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 equivalent also to the classification of the spherical unitary dual for type E. This work completes the classification of the Whittaker Iwahori-spherical unitary dual, or equivalently, the spherical unitary dual, of split linear algebraic p-adic groups.