A probabilistic approach toward conjugacy classes in the finite general linear and unitary groups

DOI10.1006/jabr.1998.7659zbMath0980.20036OpenAlexW1978726641MaRDI QIDQ1284243

Jason Fulman

Publication date: 28 February 2002

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

Full work available at URL: https://doi.org/10.1006/jabr.1998.7659

zbMATH Keywords

partitionsalgorithmsconjugacy classesgeneral linear groupsunitary groupssymmetric functionsdiscrete probability measuresnumbers of unipotent elements

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Linear algebraic groups over finite fields (20G40) Probabilistic methods in group theory (20P05)

Related Items (18)

Infinite 𝑝-adic random matrices and ergodic decomposition of 𝑝-adic Hua measures ⋮ Cohen Lenstra partitions and mutually annihilating matrices over a finite field ⋮ Binomial transforms and integer partitions into parts of \(k\) different magnitudes ⋮ Universality for cokernels of random matrix products ⋮ On the distribution of eigenspaces in classical groups over finite rings. ⋮ Cycle indices for finite orthogonal groups of even characteristic ⋮ On the distribution of the number of fixed vectors for the finite classical groups ⋮ Limits and fluctuations of \(p\)-adic random matrix products ⋮ Random matrix theory over finite fields ⋮ Random partitions and Cohen-Lenstra heuristics ⋮ The Cohen-Lenstra heuristic: methodology and results ⋮ Moments and interpretations of the Cohen-Lenstra-Martinet heuristics ⋮ \(\operatorname{GL}_n(\mathbb{F}_q)\)-analogues of factorization problems in the symmetric group ⋮ Law of large numbers for infinite random matrices over a finite field ⋮ The eigenvalue distribution of a random unipotent matrix in its representation on lines ⋮ A probabilistic approach to conjugacy classes in the finite symplectic and orthogonal groups ⋮ Finite affine groups: cycle indices, Hall-Littlewood polynomials, and probabilistic algorithms ⋮ Hall-Littlewood polynomials and Cohen-Lenstra heuristics for Jacobians of random graphs

Cites Work

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• A \(q\)-analog of the hook walk algorithm for random Young tableaux
• Some asymptotic results on finite vector spaces
• A Note on Counting Nilpotent Matrices of Fixed Rank
• Cycle indices for the finite classical groups
• The Rogers-Ramanujan identities, the finite general linear groups, and the Hall-Littlewood polynomials
• On the conjugacy classes in the unitary, symplectic and orthogonal groups

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