Skip to main content Accessibility help
×
Home

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

  • Jianbei An (a1) and Yun Gao (a1)

Abstract

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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

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

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

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

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

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

Copyright

References

Hide All
1. An, Jianbei, Weights for classical groups, Trans. Amer. Math., Soc. 342(1994), 142.
2. An, Jianbei, Weights for the Chevalley groups G2﹛q), Proc. London Math. Soc. 69(1994), 2246.3
3. An, Jianbei, Alperin-McKay conjecture for the Chevalley groups G2﹛q), J., Algebra 165(1994), 184193.
4. An, Jianbei, Dade's Conjecture for the Ree groups 2F4(q2) in non-defining characteristics, submitted.
5. Aschbacher, M., Chevalley groups of type G2 as the group of a trilinear form, J., Algebra 109(1987), 193259.
6. Broué, M., Isometries parfaites, types de blocs, catégories dérivées, Asterisque 181— 182(1990), 6192.
7. Broué, M. and Michel, J., Blocs et séries de Lusztig dans un groupe réductif J. Reine Angew., Math. 395(1989), 5667.
8. Burgoyne, N. and Williamson, C., On a theorem ofBorel and Tits for finite Chevalley groups, Arch. Math., (Basel) 27(1976), 489491.
9. Cananes, M. and Enguehard, M., Unipotent blocks of finite reductive groups of a given type, Math., Z. 213(1993), 479490.
10. Dade, E., Counting characters in blocks, I, Invent., Math. 109(1992), 187210.
11. Digne, F. and Michel, J., Foncteurs de Lusztig et charactéres des groups linéaires et unitaires sur corps fini, J., Algebra 107(1987), 217255.
12. Feit, W., The representation theory of finite groups, North Holland, 1982.
13. Fong, P. and Srinivasan, B., The blocks of finite general linear and unitary groups, Invent., Math. 69(1982), 109153.
14. Fulton, W. and Harris, J., Representation theory, Springer-Verlag, 1991.
15. Hiss, G., On the decomposition numbers ofG2(q), J., Algebra 120(1989), 339360.
16. Hiss, G. and Shamash, J., 3-blocks and 3-modular characters ofG2(q), J., Algebra 131(1990), 371387.
17. Hiss, G., 2-blocks and 2-modular characters of the Chevalley groups G2(q), Math., Comp. 59(1992), 645- 672.
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), 3071.
19. Lusztig, G., On the representations of reductive groups with disconnected center,, Asterisque 168(1988), 157166.
20. Malle, G., The maximal subgroups of2 F4(q2), J., Algebra 139(1989), 5269.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

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

  • Jianbei An (a1) and Yun Gao (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed