Whittaker unitary dual of affine graded Hecke algebras of type E

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.Comment: 48 page

Ladder representations of GL(n,Q_p)

In this paper, we recover certain known results about the ladder representations of GL(n, Q_p) defined and studied by Lapid, Minguez, and Tadic. We work in the equivalent setting of graded Hecke algebra modules. Using the Arakawa-Suzuki functor from category O to graded Hecke algebra modules, we show that the determinantal formula proved by Lapid-Minguez and Tadic is a direct consequence of the BGG resolution of finite dimensional simple gl(n)-modules. We make a connection between the semisimplicity of Hecke algebra modules, unitarity with respect to a certain hermitian form, and ladder representations.Comment: 14 page

Hermitian forms for affine Hecke algebras

We study star operations for Iwahori-Hecke algebras and invariant hermitian forms for finite dimensional modules over (graded) affine Hecke algebras with a view towards a unitarity algorithm.Comment: 29 pages, preliminary version. v2: the classification of star operations for the graded Hecke algebras and the construction of hermitian forms in the Iwahori case via Bernstein's projectives have been removed from this preprint and they will make the basis of a new pape

Dirac cohomology of unipotent representations of Sp(2n,R) and U(p,q)

In this paper we study the problem of computing the Dirac cohomology of the special unipotent representations of the real groups Sp(2n,R) and U(p,q)

Algebraic Families of Groups and Commuting Involutions

Let $G$ be a complex affine algebraic group, and let $\sigma_1$ and $\sigma_2$ be commuting anti-holomorphic involutions of $G$. We construct an algebraic family of algebraic groups over the complex projective line and a real structure on the family that interpolates between the real forms $G^{\sigma_1}$ and $G^{\sigma_2}$