Hostname: page-component-f554764f5-rj9fg Total loading time: 0 Render date: 2025-04-08T19:16:49.603Z Has data issue: false hasContentIssue false
  • English
  • Français

Character tables of the maximal parabolic subgroups of the Ree groups 2F4(q2)

Part of: Representation theory of groups

Published online by Cambridge University Press:  01 April 2010

Frank Himstedt  and
Shih-Chang Huang
Frank Himstedt
Affiliation:
Technische Universität München, Zentrum Mathematik – SB-S-MA, Boltzmannstrasse 3, 85748 Garching, Germany (email: [email protected])http://www-m11.ma.tum.de/∼himstedt
Shih-Chang Huang
Affiliation:
Department of Mathematics, National Cheng Kung University, No. 1 Dasyue Rd, Tainan City 70101, Taiwan (email: [email protected])http://www.math.ncku.edu.tw/∼shuang/

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We compute the conjugacy classes of elements and the character tables of the maximal parabolic subgroups of the simple Ree groups 2F4(q2). For one of the maximal parabolic subgroups, we find an irreducible character of the unipotent radical that does not extend to its inertia subgroup.

MSC classification

Secondary: 20C33: Representations of finite groups of Lie type 20C40: Computational methods
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 13 , January 2010 , pp. 90 - 110
Copyright
Copyright © London Mathematical Society 2010

References

[1] Carter, R., Finite groups of Lie type – conjugacy classes and complex characters (Wiley–Interscience, Chichester, 1985).Google Scholar
[2] Char, B. W., Geddes, K. O., Gonnet, G. H., Leong, B. L., Monagan, M. B. and Watt, S. M., Maple V, language reference manual (Springer, New York, 1991).CrossRefGoogle Scholar
[3] Digne, F. and Michel, J., Representations of finite groups of Lie type (Cambridge University Press, Cambridge, 1990).Google Scholar
[4] Enomoto, H. and Yamada, H., ‘The characters of the finite group G 2(2n)’, Jpn. J. Math. 12 (1986) 325–377.CrossRefGoogle Scholar
[5] The GAP Group, ‘GAP – Groups, algorithms, and programming’, version 4.4.12 (2008),http://www.gap-system.org.Google Scholar
[6] Geck, M., Hiss, G., Lübeck, F., Malle, G. and Pfeiffer, G., ‘CHEVIE – A system for computing and processing generic character tables for finite groups of Lie type, Weyl groups and Hecke algebras’, Appl. Algebra Eng. Comm. Comput. 7 (1996) 175–210.CrossRefGoogle Scholar
[7] Himstedt, F., ‘Character tables of parabolic subgroups of Steinberg’s triality groups’, J. Algebra 281 (2004) 774–822.CrossRefGoogle Scholar
[8] Himstedt, F., ‘Character tables of parabolic subgroups of Steinberg’s triality groups 3D 4(2n)’, J. Algebra 316 (2007) 254–283.CrossRefGoogle Scholar
[9] Himstedt, F., ‘On the 2-decomposition numbers of Steinberg’s triality groups 3D 4(q), q odd’, J. Algebra 309 (2007) 569–593.CrossRefGoogle Scholar
[10] Himstedt, F. and Huang, S.-C., ‘Character table of a Borel subgroup of the Ree groups 2F 4(q 2)’, LMS J. Comput. Math. 12 (2009) 1–53.CrossRefGoogle Scholar
[11] Himstedt, F., Nguyen, H. N. and Tiep, P. H., ‘On the restriction of cross characteristic representations of 2F 4(q) to proper subgroups’, Arch. Math. 93 (2009) 415–423.CrossRefGoogle Scholar
[12] Huang, S.-C., ‘Dade’s invariant conjecture for the Chevalley groups of type G 2 in the defining characteristic’, J. Algebra 292 (2005) 110–121.CrossRefGoogle Scholar
[13] Isaacs, M., Character theory of finite groups (Dover, New York, 1976).Google Scholar
[14] Malle, G., ‘Die unipotenten Charaktere von 2F 4(q 2)’, Comm. Algebra 18 (1990) 2361–2381.CrossRefGoogle Scholar
[15] Nguyen, H. and Tiep, P., ‘Cross characteristic representations of 3D 4(q) are reducible over proper subgroups’, J. Group Theory 11 (2008) 657–668.CrossRefGoogle Scholar
[16] Späth, B., ‘The McKay-conjecture for exceptional groups and odd primes’, Math. Z. 261 (2009) 571–595.CrossRefGoogle Scholar
[17] Suzuki, M., ‘On a class of doubly transitive groups’, Ann. of Math. (2) 75 (1962) 105–145.CrossRefGoogle Scholar
[18] Waki, K., ‘A note on decomposition numbers of G 2(2n)’, J. Algebra 274 (2004) 602–606.CrossRefGoogle Scholar
Supplementary material: File

Himstedt supplementary material

Appendix tables 5 & 9

Download Himstedt supplementary material(File)
File 240.1 KB