• Corpus ID: 232185657

# Trou spectral dans les groupes simples

@inproceedings{He2020TrouSD,
title={Trou spectral dans les groupes simples},
author={Weikun He and Nicolas de Saxc'e},
year={2020}
}
• Published 11 March 2021
• Mathematics
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.

## References

SHOWING 1-10 OF 67 REFERENCES
Expansion in perfect groups
• Mathematics
• 2012
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
• Mathematics
Compositio Mathematica
• 2015
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
Affine linear sieve, expanders, and sum-product
• Mathematics
• 2010
AbstractLet $\mathcal{O}$ be an orbit in ℤn of a finitely generated subgroup Λ of GLn(ℤ) whose Zariski closure Zcl(Λ) is suitably large (e.g. isomorphic to SL2). We develop a Brun combinatorial
Dynamical properties of profinite actions
• Mathematics
Ergodic Theory and Dynamical Systems
• 2011
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
Congruence Properties of Zariski‐Dense Subgroups I
• Mathematics
• 1984
This paper deals with the following general situation: we are given an algebraic group G defined over a number field K, and a subgroup F of the group G(K) of K-rational points of G. Then what should
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 $SU(d)$
• Mathematics
• 2011
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
• Mathematics
• 2011
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
On the minimal degrees of projective representations of the finite Chevalley groups
• Mathematics
• 1974
For G = G(q), a Chevalley group defined over the field iFQ of characteristic p, let Z(G,p) be th e smallest integer t > 1 such that G has a projective irreducible representation of degree t over a