135
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

On the Decomposition Numbers of Steinberg's Triality Groups 3D4(2n) in Odd Characteristics

&
Pages 1484-1498 | Received 25 Apr 2011, Published online: 02 Apr 2013

REFERENCES

  • Bonnafé , C. , Rouqier , R. ( 2003 ). Catégories dérivées et variétés de Deligne-Lusztig . Publ. Math. IHES 97 : 1 – 59 .
  • Cabanes , M. , Enguehard , M. ( 2004 ). Representation Theory of Finite Reductive Groups . Cambridge University Press .
  • Carter , R. W. ( 1985 ). Finite Groups of Lie Type – Conjugacy Classes and Complex Characters . Chichester : A Wiley-Interscience Publication .
  • Deriziotis , D. I. , Michler , G. O. ( 1987 ). Character tables and blocks of finite simple triality groups 3 D 4(q) . Trans. Amer. Math. Soc. 303 : 39 – 70 .
  • Dipper , R. ( 1990 ). On quotients of Hom-functors and representations of finite general linear groups I . J. Algebra 130 : 235 – 259 .
  • The GAP Group . ( 2008 ). GAP – Groups, Algorithms, and Programming, Version 4.4.12. Available at http://www.gap-system.org .
  • Geck , M. ( 1990 ). Verallgemeinerte Gelfand-Graev Charaktere und Zerlegungszahlen endlicher Gruppen von Lie-Typ. Dissertation, RWTH Aachen .
  • Geck , M. (1991). Generalized Gelfand-Graev characters for Steinberg's triality groups and their applications. Comm. Algebra 19:3249–3269.
  • Geck , M. , Hiss , G. ( 1997 ). Modular representations of finite groups of Lie type in non-defining characteristic . In: Cabanes , M. , ed. Finite Reductive Groups: Related Structures and Representations . Basel : Birkhäuser , pp. 195 – 249 .
  • Geck , M. , Hiss , G. , Lübeck , F. , Malle , G. , Pfeiffer , G. ( 1996 ). CHEVIE – A system for computing and processing generic character tables for finite groups of Lie type, Weyl groups and Hecke algebras . Appl. Algebra Engrg. Comm. Comput. 7 : 175 – 210 .
  • Himstedt , F. ( 2007 ). Character tables of parabolic subgroups of Steinberg's triality groups 3 D 4(2 n ) . J. Algebra 3161 : 254 – 283 .
  • Himstedt , F. ( 2007 ). On the 2-decomposition numbers of Steinberg's triality groups 3 D 4(q), q odd . J. Algebra 309 : 569 – 593 .
  • Himstedt , F. ( 2011 ). On the decomposition numbers of the Ree groups 2 F 4(q 2) in non-defining characteristic . J. Algebra 325 : 364 – 403 .
  • Hiss , G. ( 1989 ). Zerlegungszahlen Endlicher Gruppen vom Lie-Typ in Nicht-Definierender Charakteristik. Habilitationsschrift, RWTH Aachen .
  • Hiss , G. ( 1993 ). Harish-Chandra series of Brauer characters in a finite group with a split BN-pair . J. London Math. Soc. 48 : 219 – 228 .
  • Hiss , G. ( 2004 ). Hermitian function fields, classical unitals, and representations of 3-dimensional unitary groups . Indag. Math. (N. S.) 15 : 223 – 243 .
  • Hisst , G. , Lux , K. ( 1989 ). Brauer Trees of Sporadic Groups . Oxford : Oxford University Press .
  • Hiss , G. , Malle , G. ( 2001 ). Low-dimensional representations of quasi-simple groups . LMS J. Comput. Math. 4 : 22 – 63 .
  • James , G. ( 1990 ). The decomposition matrices of GL n (q) for n ≤ 10 . Proc. London Math. Soc. 60 ( 3 ): 225 – 265 .
  • Jansen , C. , Lux , K. , Parker , R. , Wilson , R. ( 1995 ). An Atlas of Brauer Characters . Oxford : Clarendon Press .
  • Köhler , C. ( 2006 ). Unipotente Charaktere und Zerlegungszahlen der Endlichen Chevalleygruppen vom Typ F 4. Dissertation, RWTH Aachen .
  • Landrock , P. , Michler , G. O. ( 1980 ). Principal 2-blocks of the simple groups of Ree type . Trans. Amer. Math. Soc. 260 : 83 – 111 .
  • Lübeck , F. ( 2001 ). Small degree representations of finite Chevalley groups in defining characteristic . LMS J. Comput. Math. 4 : 135 – 169 .
  • Lübeck , F. ( 2001 ). Smallest degrees of representations of exceptional groups of Lie type . Comm. Algebra 29 ( 5 ): 2147 – 2169 .
  • Lusztig , G. ( 1980 ). On the unipotent characters of the exceptional groups over finite fields . Invent. Math. 60 : 173 – 192 .
  • Magaard , K. , Malle , G. , Tiep , P. H. ( 2002 ). Irreducibility of tensor squares, symmetric squares, and alternating squares . Pacific J. Math. 202 : 379 – 427 .
  • Okuyama , T. , Waki , K. ( 1998 ). Decomposition numbers of Sp(4, q) . J. Algebra 199 : 544 – 555 .
  • Okuyama , T. , Waki , K. ( 2002 ). Decomposition numbers of SU 3(q 2) . J. Algebra 255 : 258 – 270 .
  • Spaltenstein , N. ( 1982 ). Caractères unipotents de 3 D 4(q) . Comment. Math. Helvitici 57 : 676 – 691 .
  • Tiep , P. H. ( 2003 ). Low dimensional representations of finite quasisimple groups . In: et al. , eds. Proceedings of the London Math. Soc. Symposium “Groups, Geometries and Combinatorics” . Durham , July 2001, N.J. : World Scientific , pp. 277 – 294 .
  • Tiep , P. H. , Zalesskii , A. E. ( 2000 ). Some aspects of finite linear groups: A survey . J. Math. Sciences 100 : 1893 – 1914 .
  • Waki , K. ( 2004 ). A note on decomposition numbers of G 2(2 n ) . J. Algebra 274 : 602 – 606 .
  • Communicated by P. Tiep.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.