Finite affine groups: cycle indices, Hall-Littlewood polynomials, and probabilistic algorithms

DOI10.1006/jabr.2001.9104zbMath1008.20042arXivmath/0009182OpenAlexW1994631396MaRDI QIDQ1604369

Jason Fulman

Publication date: 4 July 2002

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0009182

zbMATH Keywords

partitionsgenerating functionsconjugacy classesrandom matricesclassical groupsRogers-Ramanujan identitiessymmetric functionsprobability measuresaffine groupsHall-Littlewood polynomialssemisimple elements

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Symmetric functions and generalizations (05E05) Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05) Generators, relations, and presentations of groups (20F05) Random matrices (algebraic aspects) (15B52) Probabilistic methods in group theory (20P05)

Related Items (3)

Proportion of cyclic matrices in maximal reducible matrix algebras ⋮ On the number of derangements and derangements of prime power order of the affine general linear groups ⋮ Random matrix theory over finite fields

Cites Work

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• A Recognition Algorithm for Special Linear Groups
• Cycle indices for the finite classical groups
• Counting cyclic and separable matrices over a finite field
• Cyclic Matrices Over Finite Fields
• Random matrix theory and \(L\)-functions at \(s=1/2\).
• Random matrix theory and \(\zeta(1/2+it)\).

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