• Corpus ID: 232185657

Trou spectral dans les groupes simples

  title={Trou spectral dans les groupes simples},
  author={Weikun He and Nicolas de Saxc'e},
Nous montrons la propri\'et\'e du trou spectral pour la famille des graphes de Cayley obtenus par r\'eduction modulo $q$ d'un sous-groupe de $\mathrm{SL}_d(\mathbb{Z})$ dont l'adh\'erence de Zariski est un $\mathbb{Q}$-groupe simple. -- We show a spectral gap property for the family of Cayley graphs obtained by reduction modulo $q$ of a subgroup of $\mathrm{SL}_d(\mathbb{Z})$ whose Zariski closure is a simple $\mathbb{Q}$-group. 

Figures from this paper



Expansion in perfect groups

Let Γ be a subgroup of $${{\rm GL}_d(\mathbb{Z}[1/q_0])}$$ generated by a finite symmetric set S. For an integer q, denote by πq the projection map $${\mathbb{Z}[1/q_0] \to \mathbb{Z}[1/q_0]/q

Diophantine properties of nilpotent Lie groups

A finitely generated subgroup ${\rm\Gamma}$ of a real Lie group $G$ is said to be Diophantine if there is ${\it\beta}>0$ such that non-trivial elements in the word ball $B_{{\rm\Gamma}}(n)$ centered

Dynamical properties of profinite actions

Abstract We study profinite actions of residually finite groups in terms of weak containment. We show that two strongly ergodic profinite actions of a group are weakly equivalent if and only if they

Kirillov theory for compact $p$-adic groups.

The purpose here is to describe a method by which one may obtain a reasonably explicit and "global" picture of the unitary representation theory of compact p-adic groups, and to indicate some

A Spectral Gap Theorem in $SU(d)$

We establish the spectral gap property for dense subgroups of $SU(d)$ ($d\geq 2$), generated by finitely many elements with algebraic entries; this result was announced in [BG3]. The method of proof

Stationary measures and equidistribution for orbits of nonabelian semigroups on the torus

Let Γ be a semigroup of d × d nonsingular integer matrices, and consider the action of Γ on the torus T. We assume throughout that the action is strongly irreducible: there is no subtorus invariant

Approximate subgroups and super-strong approximation

Surveying some of the recent developments on approximate subgroups and super-strong approximation for thin groups, we describe the Bourgain-Gamburd method for establishing spectral gaps for finite

Additive combinatorics

  • T. TaoV. Vu
  • Mathematics
    Cambridge studies in advanced mathematics
  • 2007
The circle method is introduced, which is a nice application of Fourier analytic techniques to additive problems and its other applications: Vinogradov without GRH, partitions, Waring’s problem.

A course in abstract harmonic analysis

Banach Algebras and Spectral Theory Banach Algebras: Basic Concepts Gelfand Theory Nonunital Banach Algebras The Spectral Theorem Spectral Theory of *-Representations Von Neumann Algebras Notes and

Introduction to Affine Group Schemes

I The Basic Subject Matter.- 1 Affine Group Schemes.- 1.1 What We Are Talking About.- 1.2 Representable Functors.- 1.3 Natural Maps and Yoneda's Lemma.- 1.4 Hopf Algebras.- 1.5 Translating from