820 research outputs found
The local character expansion near a tame, semisimple element
Consider the character of an irreducible admissible representation of a
p-adic reductive group. The Harish-Chandra-Howe local expansion expresses this
character near a semisimple element as a linear combination of Fourier
transforms of nilpotent orbital integrals. Under mild hypotheses, we describe
an explicit region on which the local character expansion is valid. We assume
neither that the group is connected nor that the underlying field has
characteristic zero.Comment: 20 pages; final version; reference and comments updated; section and
bibliography order changed; one typo correcte
Lifting representations of finite reductive groups II: Explicit conorms
Let be a field, a connected reductive -quasisplit group,
a finite group that acts on via -automorphisms
satisfying a quasi-semisimplicity condition, and the connected part of the
group of -fixed points of , also assumed -quasisplit. In
an earlier work, the authors constructed a canonical map
from the set of stable semisimple conjugacy classes in the dual to the
set of such classes in . We describe several situations where
can be refined to an explicit function on points, or where
it factors through such a function
Depth-zero base change for unramified U(2,1)
We give an explicit description of L-packets and quadratic base change for
depth-zero representations of unramified unitary groups in two and three
variables. We show that this base change is compatible with unrefined minimal
K-types.Comment: 30 pages; uses LaTeX packages graphics (for a rotated table) and xy
(for a diagram
On Kostant Sections and Topological Nilpotence
Let G denote a connected, quasi-split reductive group over a field F that is
complete with respect to a discrete valuation and that has a perfect residue
field. Under mild hypotheses, we produce a subset of the Lie algebra g(F) that
picks out a G(F)-conjugacy class in every stable, regular, topologically
nilpotent conjugacy class in g(F). This generalizes an earlier result obtained
by DeBacker and one of the authors under stronger hypotheses. We then show that
if F is p-adic, then the characteristic function of this set behaves well with
respect to endoscopic transfer.Comment: 23 pages, accepted for publication in the Journal of the London
Mathematical Societ
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