21 citations · 55 across the 14 of their papers we have counts for
15 papers
Jordan decompositions in Lie algebras and their duals
Loren Spice, Cheng-Chiang Tsai
We provide a discussion of Jordan decompositions in the Lie algebra, and the dual Lie algebra, of a reductive group in as uniform a way as possible. We give a counterexample to the…
On smooth-group actions on reductive groups and spherical buildings
Jeffrey D. Adler, Joshua M. Lansky, Loren Spice
Let be a field, and suppose that is a smooth -group that acts on a connected, reductive -group . Let denote the maximal smooth, connected subgroup o…
Explicit asymptotic expansions in p-adic harmonic analysis II
Loren Spice
We unwind the induction implicit in the "one-step" asymptotic expansions of arXiv:1701.02417 to describe how to turn asymptotic expansions, such as (but not limited to) the Harish-…
A twisted Yu construction, Harish-Chandra characters, and endoscopy
Jessica Fintzen, Tasho Kaletha, Loren Spice
We give a modification of Yu's construction of supercuspidal representations of a connected reductive group over a non-archimedean local field. This modification restores the valid…
The Bernstein projector determined by a weak associate class of good cosets
Yeansu Kim, Loren Spice, Sandeep Varma
Let be a reductive group over a -adic field of characteristic zero, with . In [Kim04], J.-L. Kim studied an equivalence relation called weak associativity on th…
On certain sign characters of tori and their extensions to Bruhat-Tits groups
Jessica Fintzen, Tasho Kaletha, Loren Spice
We consider two sign characters defined on a tamely ramified maximal torus T of a twisted Levi subgroup M of a reductive p-adic group G. We show that their product extends to the s…
Explicit asymptotic expansions for tame supercuspidal characters
Loren Spice
We combine the ideas of a Harish-Chandra--Howe local character expansion, which can be centred at an arbitrary semisimple element, and a Kim--Murnaghan asymptotic expansion, which…
Stability of character sums for positive-depth, supercuspidal representations
Stephen DeBacker, Loren Spice
We re-write the character formulæ of Adler and the second-named author in a form amenable to explicit computations in -adic harmonic analysis, and use them to prove the stabilit…
On counting orbits in root systems
Loren Spice
The computation of the characters of supercuspidal representations of a p-adic group involves some 4th roots of unity whose values are defined in terms of orbits of the Galois grou…
Supercuspidal characters of over a -adic field
Jeffrey D. Adler, Stephen DeBacker, Paul J. Sally +1
The character formulas of Sally and Shalika are an early triumph in -adic harmonic analysis, but, to date, the calculations underlying the formulas have not been available. In t…
Fourier transforms of orbital integrals on the Lie algebra of
Loren Spice
The Harish-Chandra--Howe local character expansion expresses the characters of reductive, -adic groups in terms of Fourier transforms of nilpotent orbital integrals on their Lie…
On the computability of some positive-depth supercuspidal characters near the identity
Raf Cluckers, Clifton Cunningham, Julia Gordon +1
This paper is concerned with the values of Harish-Chandra characters of a class of positive-depth, toral, very supercuspidal representations of -adic symplectic and special orth…
Supercuspidal characters of reductive p-adic groups
Jeffrey D. Adler, Loren Spice
We compute the characters of many supercuspidal representations of reductive p-adic groups. Specifically, we deal with representations that arise via Yu's construction from data sa…
Topological Jordan decompositions
Loren Spice
The notion of a topological Jordan decomposition of a compact element of a reductive p-adic group has proven useful in many contexts. In this paper, we generalise it to groups defi…
Good product expansions for tame elements of reductive p-adic groups
Jeffrey D. Adler, Loren Spice
We show that, under fairly general conditions, many elements of a p-adic group can be well approximated by a product whose factors have properties that are helpful in performing ex…