Results 1 to 10 of about 663 (54)

Local newforms for the general linear groups over a non-archimedean local field

Forum of Mathematics, Pi, 2022
In [14], Jacquet–Piatetskii-Shapiro–Shalika defined a family of compact open subgroups of p-adic general linear groups indexed by nonnegative integers and established the theory of local newforms for irreducible generic representations. In this paper, we
Hiraku Atobe, Satoshi Kondo, Seidai Yasuda   +2 more
doaj   +1 more source

On Sarnak’s Density Conjecture and Its Applications

Forum of Mathematics, Sigma, 2023
Sarnak’s density conjecture is an explicit bound on the multiplicities of nontempered representations in a sequence of cocompact congruence arithmetic lattices in a semisimple Lie group, which is motivated by the work of Sarnak and Xue ([58]).
Konstantin Golubev, Amitay Kamber
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Finiteness properties of the category of mod p representations of ${\textrm {GL}}_2 (\mathbb {Q}_{p})$

Forum of Mathematics, Sigma, 2021
We establish the Bernstein-centre type of results for the category of mod p representations of $\operatorname {\mathrm {GL}}_2 (\mathbb {Q}_p)$ . We treat all the remaining open cases, which occur when p is $2$ or $3$ .
Vytautas Paškūnas, Shen-Ning Tung
doaj   +1 more source

ON THE EXISTENCE OF ADMISSIBLE SUPERSINGULAR REPRESENTATIONS OF $p$-ADIC REDUCTIVE GROUPS

Forum of Mathematics, Sigma, 2020
Suppose that $\mathbf{G}$ is a connected reductive group over a finite extension $F/\mathbb{Q}_{p}$ and that $C$ is a field of characteristic $p$. We prove that the group $\mathbf{G}(F)$ admits an irreducible admissible supercuspidal, or equivalently ...
FLORIAN HERZIG, KAROL KOZIOŁ, MARIE-FRANCE VIGNÉRAS   +2 more
doaj   +1 more source

WAVE FRONT HOLONOMICITY OF $\text{C}^{\text{exp}}$-CLASS DISTRIBUTIONS ON NON-ARCHIMEDEAN LOCAL FIELDS

Forum of Mathematics, Sigma, 2020
Many phenomena in geometry and analysis can be explained via the theory of $D$-modules, but this theory explains close to nothing in the non-archimedean case, by the absence of integration by parts. Hence there is a need to look for alternatives.
AVRAHAM AIZENBUD, RAF CLUCKERS
doaj   +1 more source

Equivariant perverse sheaves on Coxeter arrangements and buildings [PDF]

Épijournal de Géométrie Algébrique, 2019
When $W$ is a finite Coxeter group acting by its reflection representation on $E$, we describe the category ${\mathsf{Perv}}_W(E_{\mathbb C}, {\mathcal{H}}_{\mathbb C})$ of $W$-equivariant perverse sheaves on $E_{\mathbb C}$, smooth with respect to the ...
Martin H. Weissman
doaj   +1 more source

COCENTERS OF $p$ -ADIC GROUPS, I: NEWTON DECOMPOSITION

Forum of Mathematics, Pi, 2018
In this paper, we introduce the Newton decomposition on a connected reductive $p$ -adic group $G$ . Based on it we give a nice decomposition of the cocenter of its Hecke algebra. Here we
XUHUA HE
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THE BERNSTEIN CENTER OF THE CATEGORY OF SMOOTH $W(k)[\text{GL}_{n}(F)]$ -MODULES

Forum of Mathematics, Sigma, 2016
We consider the category of smooth $W(k)[\text{GL}_{n}(F)]$ -modules, where $F$
DAVID HELM
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Raising the level for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\text {GL}_{{n}}$

Forum of Mathematics, Sigma, 2014
We prove a simple level-raising result for regular algebraic, conjugate self-dual automorphic forms on $\mathrm{GL}_n$ .
JACK A. THORNE
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Local newforms for generic representations of unramified even unitary groups I: Even conductor case

Forum of Mathematics, Sigma
In this paper, we define compact open subgroups of quasi-split even unitary groups for each even non-negative integer and establish the theory of local newforms for irreducible tempered generic representations with a certain condition on the central ...
Hiraku Atobe
doaj   +1 more source