On the weak local Arthur packets conjecture for split classical groups

B Liu, CH Lo - International Mathematics Research Notices, 2024 - academic.oup.com
Recently, motivated by the theory of real local Arthur packets, making use of the wavefront
sets of representations over non-Archimedean local fields, Ciubotaru, Mason-Brown, and …

Arithmetic Wavefront Sets and Generic -packets

D Jiang, D Liu, L Zhang - arXiv preprint arXiv:2207.04700, 2022 - arxiv.org
Let $ G $ be a classical group defined over a local field $ F $ of characteristic zero. Let $\pi $
be an irreducible admissible representation $\pi $ of $ G (F) $, which is of Casselman …

On the upper bound of wavefront sets of representations of p-adic groups

A Hazeltine, B Liu, CH Lo, F Shahidi - arXiv preprint arXiv:2403.11976, 2024 - arxiv.org
In this paper we study the upper bound of wavefront sets of irreducible admissible
representations of connected reductive groups defined over non-Archimedean local fields of …

Maximality Properties of Generalized Springer Representations of SO (N, ℂ)

R La - International Mathematics Research Notices, 2024 - academic.oup.com
Let be a unipotent class of, an irreducible-equivariant local system on. The generalized
Springer representation appears in the top cohomology of some variety. Let be the …

Relating real and p-adic Kazhdan-Lusztig polynomials

L Barchini, PE Trapa - arXiv preprint arXiv:2402.17956, 2024 - arxiv.org
Fix an integral semisimple element $\lambda $ in the Lie algebra $\mathfrak {g} $ of a
complex reductive algebraic group $ G $. Let $ L $ denote the centralizer of $\lambda $ in …

Local character expansions via positive depth Barbasch-Moy theory

D Ciubotaru, E Okada - arXiv preprint arXiv:2307.06780, 2023 - arxiv.org
In this paper we extend Barbasch and Moy's results about the local character expansion of
depth-$0 $ representations to arbitrary depth. This leads to the definition of a graded …

Jiang's conjecture and fibers of the Barbasch-Vogan duality

B Liu, CH Lo, F Shahidi - Rad Hrvatske akademije znanosti i …, 2024 - hrcak.srce.hr
Sažetak The well-known Shahidi's conjecture says that tempered L-packets have generic
members. As a natural generalization of Shahidi's conjecture to non-tempered local Arthur …

Irreducibility of wave-front sets for depth zero cuspidal representations

A Aizenbud, D Gourevitch, E Sayag - arXiv preprint arXiv:2205.14695, 2022 - arxiv.org
We show that the results of [BM97, DeB02b, Oka, Lus85, AA07, Tay16] imply a special case
of the Moeglin-Waldspurger conjecture on wave-front sets. Namely, we deduce that for large …

On wavefront sets of global Arthur packets of classical groups: Upper bound

D Jiang, B Liu - Journal of the European Mathematical Society, 2024 - ems.press
On wavefront sets of global Arthur packets of classical groups: Upper bound Page 1 © 2024
European Mathematical Society Published by EMS Press J. Eur. Math. Soc. (Online first) DOI …

[PDF][PDF] Discipline: Mathématiques

C Qin - 2024 - chuan-qin-math.github.io
In this thesis, we give two generalizations of the Alvis-Curtis duality for Hecke algebras: a
relative version for finite Hecke algebras, based on Howlett-Lehrer's work, and an unequal …