Fuchsian groups, finite simple groups and representation varieties.

DOI10.1007/s00222-004-0390-3zbMath1134.20059OpenAlexW2001825657MaRDI QIDQ1770266

Aner Shalev, Martin W. Liebeck

Publication date: 14 April 2005

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10044/1/88

zbMATH Keywords

finite simple groupsirreducible complex charactersFuchsian groupsasymptotic estimateszeta functionsrandom generationsimple algebraic groupsLang-Weil estimatesdimensions of representation varietiesrandomly chosen homomorphismsspaces of homomorphisms

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Simple groups (20E32) Group actions on varieties or schemes (quotients) (14L30) Other Dirichlet series and zeta functions (11M41) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Simple groups: alternating groups and groups of Lie type (20D06) Representations of finite groups of Lie type (20C33) Probabilistic methods in group theory (20P05)

Related Items (52)

Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements ⋮ Beauville surfaces and finite simple groups ⋮ Representation growth and rational singularities of the moduli space of local systems ⋮ Counting points of schemes over finite rings and counting representations of arithmetic lattices ⋮ Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks. ⋮ Linear groups with Borel's property ⋮ Determining Fuchsian groups by their finite quotients ⋮ Counting surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group with motivations from string theory and QFT ⋮ Triangle groups and PSL2(q) ⋮ Representation variety of Fuchsian groups in \(\mathrm{SO}(p,q)\) ⋮ Elements of specified order in simple algebraic groups ⋮ Finite covers of random 3-manifolds ⋮ On the involution fixity of exceptional groups of Lie type ⋮ New Beauville surfaces and finite simple groups ⋮ Appendix to the paper ``Some uniserial representations of certain special linear groups by P. Sin and J. G. Thompson. ⋮ Covering and growth for group subsets and representations ⋮ CHARACTER STACKS ARE PORC COUNT ⋮ The dimension of solution sets to systems of equations in algebraic groups ⋮ The finite and solvable genus of finitely generated free and surface groups ⋮ Asymptotics and Local Constancy of Characters of p-adic Groups ⋮ Character estimates for finite simple groups and applications ⋮ Products of normal subsets ⋮ Counting irreducible modules for profinite groups ⋮ Almost independence and irreducibility in simple finite and algebraic groups ⋮ Mixing, Communication Complexity and Conjectures of Gowers and Viola ⋮ The growth of abelian sections ⋮ Fibers of word maps and some applications. ⋮ Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics. ⋮ Most words are geometrically almost uniform ⋮ Triangle generation of finite exceptional groups of low rank. ⋮ On the finite simple images of free products of finite groups ⋮ Mixing and generation in simple groups. ⋮ Some remarks on global/local conjectures ⋮ Conjugacy classes, growth and complexity ⋮ Words and mixing times in finite simple groups. ⋮ ALGEBRO-GEOMETRIC INVARIANTS OF GROUPS (THE DIMENSION SEQUENCE OF A REPRESENTATION VARIETY) ⋮ Generators and commutators in finite groups; abstract quotients of compact groups. ⋮ Character ratios, representation varieties and random generation of finite groups of Lie type ⋮ Word maps, conjugacy classes, and a noncommutative Waring-type theorem. ⋮ Probabilistic Waring problems for finite simple groups ⋮ On the diameters of McKay graphs for finite simple groups ⋮ Mixed Hodge polynomials of character varieties. With an appendix by Nicholas M. Katz. ⋮ Characters of symmetric groups: sharp bounds and applications. ⋮ A generalization of the diameter bound of Liebeck and Shalev for finite simple groups ⋮ Applications of character theory of finite simple groups ⋮ Word maps and Waring type problems ⋮ Girth, words and diameter ⋮ Commutator maps, measure preservation, and 𝑇-systems ⋮ Random and Deterministic Triangle Generation of Three-Dimensional Classical Groups I ⋮ Probabilistic and Asymptotic Aspects of Finite Simple Groups ⋮ Beauville Surfaces and Probabilistic Group Theory ⋮ Surfaces Isogenous to a Product of Curves, Braid Groups and Mapping Class Groups

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