23
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

RESTRICTIONS OF LARGE IRREDUCIBLE REPRESENTATIONS OF THE CLASSICAL GROUPS TO NATURALLY EMBEDDED SMALL SUBGROUPS CANNOT BE SEMISIMPLE

Pages 3747-3757 | Received 01 Jan 2001, Published online: 01 Feb 2007

REFERENCES

  • Borel , A. 1970 . “ Properties and Linear Representations of Chevalley Groups ” . In Seminar on Algebraic Groups and Related Finite Groups Vol. 131 , 1 – 55 . Lecture Notes in Math. Springer-Verlag .
  • Bourbaki , N. 1968 . Groupes et Algebres de Lie. Ch. IV–VI Paris : Hermann .
  • Brundan , J. , Kleshchev , A. S. and Suprunenko , I. D. 1998 . Semisimple Restrictions from GL(n) to GL(n−1) . J. fur die Reine und Ungew. Math. , 500 : 83 – 112 .
  • Chevalley , C. 1954 . Theorie des Groupes de Lie Vol. III , Paris : Hermann .
  • Guralnick , R. M. 1999 . Small Representations are Completely Reducible . J. Algebra , 220 ( 2 ) : 531 – 541 .
  • Jantzen , J. C. 1996 . “ Low Dimensional Representations of Algebraic Groups are Semisimple ” . In Algebraic Groups and Related Subjects; a Volume in Honour of R.W. Richardson 255 – 266 . Austral. Math. Soc. Lect. Ser. Cambridge Univ. Press .
  • McNinch , G. J. 1998 . Dimensional Criteria for Semisimplicity of Representations . Proc. London Math. Soc. , 76 : 95 – 149 .
  • McNinch , G. J. 1998 . “ Semisimplicity in Positive Characteristic ” . In Algebraic Groups and their Representations Vol. 517 , 43 – 52 . Dordrecht : NATO ASI Ser.C.: Math. and Phys. Sci. Kluwer Academic Publishers .
  • McNinch , G. J. 1999 . Semisimple Modules for Finite Groups of Lie Type . J. London Math. Soc. , 60 ( 2 ) : 771 – 792 .
  • McNinch , G. J. 2000 . Semisimplicity of Exterior Powers of Semisimple Representations of Groups . J. Algebra , 225 ( 2 ) : 646 – 666 .
  • Seitz , G. M. 1987 . The Maximal Subgroups of Classical Algebraic Groups . Mem. Amer. Math. Soc. , 365
  • Serre , J.-P. 1994 . Sur la Semi-simplicite des Produits Tensoriels de Representations de Groupes . Invent. Math. , 116 : 513 – 530 .
  • Serre , J.-P. Moursund lectures 1998. Part II. The Notion of Complete Reducibility in Group Theory . notes by W.E. Duckworth, Univ. Oregon Math. Dept. http://darkwing.uoregon.edu/math/serre/index.html
  • Smith , S. 1982 . Irreducible Modules and Parabolic Subgroups . J. Algebra , 75 : 286 – 289 .
  • Steinberg , R. 1968 . Lectures on Chevalley Groups New Haven : Yale University .
  • Steinberg , R. 1963 . Representations of Algebraic Groups . Nagoya Math. J. , 22 : 33 – 56 .
  • Suprunenko , I. D. 1997 . On Jordan Blocks of Elements of Order p in Irreducible Representations of Classical Groups with p-large Highest Weights . J. Algebra , 191 : 589 – 627 .
  • Suprunenko , I. D. 1998 . Restrictions of Modular Irreducible Representations of the Special Linear Group with Large Highest Weights with Respect to Characteristic to Small Natural Subgroups are not Completely Reducible (in Russian, English summary) . Doklady Nat. Akad. Nauk Belarusi , 42 ( 3 ) : 27 – 31 .

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.