196 research outputs found
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
Star operations for affine Hecke algebras
In this paper, we consider the star operations for (graded) affine Hecke
algebras which preserve certain natural filtrations. We show that, up to inner
conjugation, there are only two such star operations for the graded Hecke
algebra: the first, denoted , corresponds to the usual star operation
from reductive -adic groups, and the second, denoted can be
regarded as the analogue of the compact star operation of a real group
considered by \cite{ALTV}. We explain how the star operation appears
naturally in the Iwahori-spherical setting of -adic groups via the
endomorphism algebras of Bernstein projectives. We also prove certain results
about the signature of -invariant forms and, in particular, about
-unitary simple modules.Comment: 27 pages; section 3 and parts of sections 2 and 5 were previously
contained in the first version of the preprint arXiv:1312.331
Asymptotic cone of semisimple orbits for symmetric pairs
Let G be a reductive algebraic group over the complex field and O_h be a
closed adjoint orbit through a semisimple element h. By a result of Borho and
Kraft (1979), it is known that the asymptotic cone of the orbit O_h is the
closure of a Richardson nilpotent orbit corresponding to a parabolic subgroup
whose Levi component is the centralizer Z_G(h) in G.
In this paper, we prove an analogue on a semisimple orbit for a symmetric
pair (G, K).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
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
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)
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