Character degrees and random walks in finite groups of Lie type

Proceedings of the London Mathematical Society

Volumn 90, Issue 1, 2005, Pages 61-86

  Liebeck, Martin W ^a   Shalev, Aner ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 28144454420     PISSN: 00246115     EISSN: 1460244X     Source Type: Journal    
DOI: 10.1112/S0024611504014935     Document Type: Article

References (43)

1. H. BASS, A. LUBOTZKY, A. R. MAGID and S. MOZES, 'The proalgebraic completion of rigid groups', Geom. Dedicata 95 (2002) 19-58.
2. T. C. BURNESS, 'Fixed point ratios in actions of finite classical groups', PhD Thesis, Imperial College, London, 2004.
3. T. C. BURNESS, M. W. LIEBECK and A. SHALEV, 'Base sizes for primitive actions of finite groups of Lie type', in preparation.
4. P. J. CAMERON, 'Some open problems on permutation groups', Groups, combinatorics and geometry (ed. M. Liebeck and J. Saxl), London Mathematical Society Lecture Note Series 165 (Cambridge University Press, 1992) 340-350.
5. P. J. CAMERON and W. M. KANTOR, 'Random permutations: some group-theoretic aspects', Combin. Probab. Comput. 2 (1993) 257-262.
6. R. W. CARTER, 'Centralizers of semisimple elements in the finite classical groups', Proc. London Math. Soc. (3) 42 (1981) 1-41.
7. R. W. CARTER, Finite groups of Lie type: conjugacy classes and complex characters (Wiley Interscience, New York, 1985).
8. D. I. DERIZIOTIS, 'On the number of conjugacy classes in finite groups of Lie type', Comm. Algebra 13 (1985) 1019-1045.
9. D. I. DERIZIOTIS and M. W. LIEBECK, 'Centralizers of semisimple elements in finite twisted groups of Lie type', J. London Math. Soc. (2) 31 (1985) 48-54.
10. P. W. DIACONIS, Group representations in probability and statistics, IMS Lecture Notes -Monograph Series 11 (Institute of Mathematical Statistics, Hayward, CA, 1988).
11. P. DIACONIS, 'Random walks on groups: characters and geometry', Groups St Andrews 2001 in Oxford I (ed. C. M. Campbell, E. F. Robertson and G. C. Smith), London Mathematical Society Lecture Note Series 304 (Cambridge University Press, 2003) 120-142.
12. P. DIACONIS and M. SHAHSHAHANI, 'Generating a random permutation with random transpositions', Z. Wahrscheinlichkeitstheorie Verw. Gebiete 57 (1981) 159-179.
13. F. DIGNE and J. MICHEL, Representations of finite groups of Lie type, London Mathematical Society Student Texts 21 (Cambridge University Press, 1991).
14. L. DORNHOFF, Group representation theory, Part A (Marcel Dekker, New York, 1971).
15. J. FULMAN and R. GURALNICK, 'Derangements in simple and primitive groups', Groups, combinatorics and geometry: Durham, 2001 (ed. A. Ivanov, M. Liebeck and J. Saxl, World Scientific, Singapore, 2003) 99-121.
16. J. FULMAN and R. GURALNICK, 'The number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements', Preprint, University of Southern California, 2004.
17. D. GLUCK, 'Characters and random walks on finite classical groups', Adv. Math. 129 (1997) 46-72.
18. D. GORENSTEIN, R. LYONS and R. SOLOMON, The classification of the finite simple groups, Vol. 3, Mathematical Surveys and Monographs 40, No. 3 (American Mathematical Society, Providence, RI, 1998).
19. R. GURALNICK and P. H. TIEP, 'Cross characteristic representations of even characteristic symplectic groups', Trans. Amer. Math. Soc. 356 (2004) 4969-5023.
20. q) by random transvections', J. Algebraic Combin. 1 (1992) 133-150.
21. I. M. ISAACS, 'Characters of solvable and symplectic groups', Amer. J. Math. 95 (1973) 594-635.
22. I. M. ISAACS, Character theory of finite groups (Academic Press, New York, 1976).
23. A. JAIKIN, 'On the characters of pro-p groups of finite rank', Preprint, University of Madrid, 2004.
24. A. JAIKIN, 'On two conditions on characters and conjugacy classes in finite soluble groups', Preprint, University of Madrid, 2004.
25. V. LANDAZURI and G. M. SEITZ, 'On the minimal degrees of projective representations of the finite Chevalley groups', J. Algebra 32 (1974) 418-443.
26. M. W. LIEBECK and L. PYBER, 'Upper bounds for the number of conjugacy classes of a finite group', J. Algebra 198 (1997) 538-562.
27. M. W. LIEBECK and A. SHALEV, 'Simple groups, permutation groups, and probability', J. Amer. Math. Soc. 12 (1999) 497-520.
28. M. W. LIEBECK and A. SHALEV, 'Diameters of finite simple groups: sharp bounds and applications', Ann. of Math. 154 (2001) 383-406.
29. M. W. LIEBECK and A. SHALEV, 'Bases of primitive permutation groups', Groups, combinatorics and geometry: Durham, 2001 (ed. A. Ivanov, M. Liebeck and J. Saxl, World Scientific, Singapore, 2003) 147-154.
30. M. W. LIEBECK and A. SHALEV, 'Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks', J. Algebra 276 (2004) 552-601.
31. M. W. LIEBECK and A. SHALEV, 'Fuchsian groups, finite simple groups and representation varieties', Invent. Math. to appear.
32. A. LUBOTZKY and B. MARTIN, 'Polynomial representation growth and the congruence subgroup property', Preprint, Hebrew University, Jerusalem, 2003.
33. N. LULOV, 'Random walks on symmetric groups generated by conjugacy classes', PhD Thesis, Harvard University, 1996.
34. G. LUSZTIG, Characters of reductive groups over a finite field, Annals of Mathematics Studies 107 (Princeton University Press, 1984).
35. G. LUSZTIG, 'On the representations of reductive groups with disconnected centre', Orbites unipotentes et représentations I, Astérisque 168, no. 10 (Société Mathématique de France, Paris, 1988) 157-166.
36. Y. ROICHMAN, 'Upper bound on the characters of the symmetric groups', Invent. Math. 125 (1996) 451-485.
37. G. M. SEITZ, 'Root groups for maximal tori in finite groups of Lie type', Pacific J. Math. 106 (1983) 153-244.
38. 2)', Canad. J. Math. 25 (1973) 486-494.
39. T. A. SPRINGER and R. STEINBERG, 'Conjugacy classes', Seminar on algebraic groups and related topics (ed. A. Borel et al.), Lecture Notes in Mathematics 131 (Springer, Berlin, 1970) 168-266.
40. P. H. TIEP and A. E. ZALESSKII, 'Minimal characters of the finite classical groups', Comm. Algebra 24 (1996) 2093-2167.
41. P. H. TIEP and A. E. ZALESSKII, 'Some characterizations of the Weil representations of the symplectic and unitary groups', J. Algebra 192 (1997) 130-165.
42. G. E. WALL, 'On the conjugacy classes in the unitary, symplectic and orthogonal groups', J. Austral. Math. Soc. 3 (1965) 1-62.
43. E. WITTEN, 'On quantum gauge theories in two dimensions', Comm. Math. Phys. 141 (1991) 153-209.