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Dade's Conjecture for Chevalley Groups G2(q) in Non-Defining Characteristics

Published online by Cambridge University Press:  20 November 2018

Jianbei An  and
Yun Gao
Jianbei An
Affiliation:
Department of Mathematics University of Auckland Private Bag 92019 Auckland, New Zealand, e-mail: an@math.auckland.ac.nz
Yun Gao
Affiliation:
Department of Mathematics University of Auckland Private Bag 92019 Auckland, New Zealand, e-mail: an@math.auckland.ac.nz
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Abstract

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This paper is part of a program to study the conjecture of E. C. Dade on counting characters in blocks for several finite groups of Lie type. The local structures of certain radical chains of Chevalley groups of type G2 are given and the ordinary conjecture is confirmed for the groups when the characteristic of the modular representation is distinct from the defining characteristic of the groups.

Keywords

20C2020G40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 4 , 01 August 1996 , pp. 673 - 691
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. An, Jianbei, Weights for classical groups, Trans. Amer. Math., Soc. 342(1994), 1–42.Google Scholar
2. An, Jianbei, Weights for the Chevalley groups G2﹛q), Proc. London Math. Soc. 69(1994), 22–46.3Google Scholar
3. An, Jianbei, Alperin-McKay conjecture for the Chevalley groups G2﹛q), J., Algebra 165(1994), 184–193.Google Scholar
4. An, Jianbei, Dade's Conjecture for the Ree groups 2F4(q2) in non-defining characteristics, submitted.Google Scholar
5. Aschbacher, M., Chevalley groups of type G2 as the group of a trilinear form, J., Algebra 109(1987), 193–259.Google Scholar
6. Broué, M., Isometries parfaites, types de blocs, catégories dérivées, Asterisque 181— 182(1990), 61–92.Google Scholar
7. Broué, M. and Michel, J., Blocs et séries de Lusztig dans un groupe réductif J. Reine Angew., Math. 395(1989), 56–67.Google Scholar
8. Burgoyne, N. and Williamson, C., On a theorem ofBorel and Tits for finite Chevalley groups, Arch. Math., (Basel) 27(1976), 489–491.Google Scholar
9. Cananes, M. and Enguehard, M., Unipotent blocks of finite reductive groups of a given type, Math., Z. 213(1993), 479–490.Google Scholar
10. Dade, E., Counting characters in blocks, I, Invent., Math. 109(1992), 187–210.Google Scholar
11. Digne, F. and Michel, J., Foncteurs de Lusztig et charactéres des groups linéaires et unitaires sur corps fini, J., Algebra 107(1987), 217–255.Google Scholar
12. Feit, W., The representation theory of finite groups, North Holland, 1982.Google Scholar
13. Fong, P. and Srinivasan, B., The blocks of finite general linear and unitary groups, Invent., Math. 69(1982), 109–153.Google Scholar
14. Fulton, W. and Harris, J., Representation theory, Springer-Verlag, 1991.Google Scholar
15. Hiss, G., On the decomposition numbers ofG2(q), J., Algebra 120(1989), 339–360.Google Scholar
16. Hiss, G. and Shamash, J., 3-blocks and 3-modular characters ofG2(q), J., Algebra 131(1990), 371–387.Google Scholar
17. Hiss, G., 2-blocks and 2-modular characters of the Chevalley groups G2(q), Math., Comp. 59(1992), 645- 672.Google Scholar
18. Kleidman, P., The maximal subgroups of the Chevalley groups G2(q) with q odd, the Ree groups 2G2(q), and their automorphism groups, J., Algebra 117(1988), 30–71.Google Scholar
19. Lusztig, G., On the representations of reductive groups with disconnected center,, Asterisque 168(1988), 157–166.Google Scholar
20. Malle, G., The maximal subgroups of2 F4(q2), J., Algebra 139(1989), 52–69.Google Scholar