66 research outputs found
Spectral correspondences for affine Hecke algebras
We introduce the notion of spectral transfer morphisms between normalized
affine Hecke algebras, and show that such morphisms induce spectral measure
preserving correspondences on the level of the tempered spectra of the affine
Hecke algebras involved. We define a partial ordering on the set of isomorphism
classes of normalized affine Hecke algebras, which plays an important role for
the Langlands parameters of Lusztig's unipotent representations.Comment: 38 pages; The ordering of the material has been improved in this
versio
Spectral transfer morphisms for unipotent affine Hecke algebras
In this paper we will give a complete classification of the spectral transfer
morphisms between the unipotent affine Hecke algebras of the various inner
forms of a given quasi-split absolutely simple algebraic group, defined over a
non-archimidean local field and split over an unramified extension
of . As an application of these results, the results of [O4] on the
spectral correspondences associated with such morphisms and some results of
Ciubotaru, Kato and Kato [CKK] we prove a conjecture of Hiraga, Ichino and
Ikeda [HII] on the formal degrees and adjoint gamma factors for all unipotent
discrete series characters of unramified simple groups of adjoint type defined
over .Comment: 61 pages; We explained the comparison with Lusztig's parameterization
of unipotent representations in more detai
A generating function for the trace of the Iwahori-Hecke algebra
The Iwahori-Hecke algebra has a ``natural'' trace . This trace is the
evaluation at the identity element in the usual interpretation of the
Iwahori-Hecke algebra as a sub-algebra of the convolution algebra of a p-adic
semi-simple group. The Iwahori-Hecke algebra contains an important commutative
sub-algebra , that was described and studied by Bernstein,
Zelevinski and Lusztig. In this note we compute the generating function for the
value of on the basis
A formula of Arthur and affine Hecke algebras
Let be tempered representations of an affine Hecke algebra with
positive parameters. We study their Euler--Poincar\'e pairing ,
the alternating sum of the dimensions of the Ext-groups. We show that can be expressed in a simple formula involving an analytic R-group,
analogous to a formula of Arthur in the setting of reductive p-adic groups. Our
proof applies equally well to affine Hecke algebras and to reductive groups
over nonarchimedean local fields of arbitrary characteristic.Comment: 22 page
Discrete series characters for affine Hecke algebras and their formal degrees
We introduce the generic central character of an irreducible discrete series
representation of an affine Hecke algebra. Using this invariant we give a new
classification of the irreducible discrete series characters for all abstract
affine Hecke algebras (except for the types E) with arbitrary positive
parameters and we prove an explicit product formula for their formal degrees
(in all cases).Comment: 68 pages, 5 figures. In the second version an appendix was adde
- …