Cycle Indices for the Finite Classical Groups

Cycle Indices for the Finite Classical Groups (1997)

Cached

Download Links

by Jason Fulman

Venue:	J. Group Theory
Citations:	18 - 14 self

BibTeX

@ARTICLE{Fulman97cycleindices,
    author = {Jason Fulman},
    title = {Cycle Indices for the Finite Classical Groups},
    journal = {J. Group Theory},
    year = {1997},
    volume = {2},
    pages = {251--289}
}

Bookmark

OpenURL

Abstract

This paper defines and develops cycle indices for the finite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include semisimplicity, regularity, regular semisimplicity, the characteristic polynomial, number of Jordan blocks, and average order of a matrix.

Citations

537	Integer partitions - Andrews, Eriksson - 2004
355	Symmetric Functions and Hall Polynomials, Second edition - Macdonald - 1995
303	Finite Groups of Lie Type - Carter - 1993
201	Finite groups of Lie type-conjugacy classes and complaex characters - Carter - 1985
133	An introduction to the theory of numbers fifth edition - Hardy, Wright - 1979
76	Group Theory I - Suzuki - 1980
69	Regular elements of semisimple algebraic Lie groups - Steinberg - 1965
64	Conjugacy classes in semisimple algebraic groups - Humphreys - 1995
47	Ordered Cycle Lengths in a Random Permutation - Shepp, Lloyd - 1966
40	Geometric Algebra - Artin - 1957
35	Combinatorial enumeration of groups, graphs, and chemical compounds”, Springer-Verlag - Pólya, Read - 1987
33	On the conjugacy classes in the unitary, symplectic and orthogonal groups - WALL - 1963
30	On the foundations of combinatorial theory. IV. Finite vector spaces and Eulerian generating functions - Goldman, Rota - 1970
23	Some asymptotic results on finite vector spaces - Stong - 1988
16	The cycle structure of a linear transformation over a finite field - Kung - 1981
16	Praeger, Cyclic matrices over finite fields - Neumann, E - 1995
11	The number of regular semisimple elements for Chevalley groups of classical type - Fleischmann, Janiszczak - 1993
10	Probability in the classical groups over finite fields: symmetric functions, stochastic algorithms and cycle indices - Fulman - 1997
10	Rational tori, semisimple orbits and the topology of hyperplane complements - Lehrer - 1992
10	The cohomology of the regular semisimple variety - Lehrer - 1998
9	The Rogers-Ramanujan identities, the finite general linear groups, and the Hall-Littlewood polynomials - Fulman - 2000
8	The probability that a matrix be nilpotent - Fine, Herstein - 1958
8	Topics in algebra. Second edition. Xerox - Herstein - 1975
8	Praeger, Cyclic matrices in classical groups over finite fields - Neumann, E
8	On the number of matrices with given characteristic polynomial - Reiner - 1961
7	The expected order of a random permutation - Goh, Schmutz - 1991
7	How random is the characteristic polynomial of a random matrix - Hansen, Schmutz - 1993
5	les groupes classiques - Dieudonne, Sur - 1967
4	On the number of nilpotent matrices with coefficients in a finite field - Gerstenhaber - 1961
4	The average order of a matrix - Stong - 1993
4	A central limit theorem on - Goh, Schmutz - 1991
3	Probabilistic measures and algorithms arising from the Macdonald symmetric functions, preprint - Fulman
3	domaine d’analyse combinatoire - Goncharov, “Du - 1944
3	A probabilistic approach toward conjugacy classes in the finite general linear and unitary groups - Fulman - 1999
2	A central limit theorem on GLn(Fq - Goh, Schmutz
1	Formes sesqulineaires et formes quadratiques (Elements de Mathematique I, livre - Bourbaki - 1959
1	A probabilistic approach toward the finite general linear and unitary groups, preprint - Fulman
1	A central limit theorem on GL n (F q - Goh, Schmutz