Abstract
Let σ be an endomorphism of a simple, simply connected, algebraic group $$\[\bar G\]$$ over K, where K is the algebraic closure of Fp, and assume the fixed point group G = $$ {\text{G = }}{\overline {\text{G}} _{\sigma }} $$ is finite and quasisimple. Write G = G(q), with q = pa and let V be an irreducible, but not necessarily absolutely irreducible, kG-module, where k denotes K or a finite subfield of K.
Research supported in part by N.S.F. grant DMS-8318037
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aschbacher, M., On the maximal subgroups of the finite classsical groups, Invent, Math., 76, (1984), 469–514.
Aschbacher, M. and Seitz, G., Involutions in Chevalley groups over fields of even order, Nagoya Math J., 63, (1976), 1–91.
Borel, A. and Tits, J., Elements unipotents et sousgroupes paraboliques de groupes reductifs, I, Invent, Math. 12 (1971), 95–104.
Burgoyne, N. and Williamson, C., Some computations involving simple Lie algebras, Proc. 2nd. Symp. Symbolic and Algebraic Manipulation, ed. S.P. Petrick, N.Y. Assoc. Computing Machinery, 1971.
Cabanes, M., Irreducible modules and Levi supplements, J. Alg. 90 (1984), 84–97.
Curtis, C.W., Modular representations of finite groups with split (B, N)-pairs, Springer Lecture Notes, 131.
Curtis, C.W., and Reiner, L, Representation theory of finite groups and associative algebras, Interscience, New York, 1962.
Curtis, C.W., and Reiner, I., Methods of representation theory with applications to finite groups and orders, Interscience, N.Y., 1981.
Dickson, L.E., Linear groups with an exposition of the Galois field theory, Dover, New York, 1962.
James, G., The representation theory of the symmetric groups, Springer-Verlag, Lecture Notes in Math., 182.
Hartley, R.W., Determination of the ternary collineation linear groups whose coefficients he in GF(2n), Annals math., 27 (1925), 140–158.
Humphreys, J., Linear algebraic groups, Springer-Verlag, New York, 1975.
Liebeck, M., Saxl, J., and Seitz, G., On the overgroups of irreducible subgroups of GL(V), (to appear).
Mitchell, H., Determination of the ordinary and modular ternary linear groups, T.A.M.S., 12, (1911), 207–242.
Seitz, G., Flag-transitive subgroups of Chevalley groups, Annals Math. 97, (1973), 27–56.
Seitz, G., Corrections to “Flag-transitive subgroups of Chevalley groups”, (notes).
Seitz, G., The maximal subgroups of classical algebraic groups, (to appear, Memoirs AMS).
Smith, S., Irreducible modules and parabolic subgroups, J. Algebra, 75, (1982), 286–289.
Steinberg, R., Representations of algebraic groups, Nagoya Math. 22, (1963), 33–56.
Suzuki, M., On a class of doubly transitive groups, Annals of Math. 12, (1960), 606–615.
Testerman, D., Certain embeddings of simple algebraic groups, Ph.D thesis, Univ. of Oregon, 1985.
Walter, J., The characterization of finite groups with abelian Sylow 2-subgroups, Annals of Math. 89 (1969), 405–514.
Ward, H. N., On Ree’s series of simple groups, T.A.M.S., 121, (1966), 62–89.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 D. Reidel Publishing Company, Dordrecht, Holland
About this paper
Cite this paper
Seitz, G.M. (1988). Representations and Maximal Subgroups of Finite Groups of Lie Type. In: Aschbacher, M., Cohen, A.M., Kantor, W.M. (eds) Geometries and Groups. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4017-8_13
Download citation
DOI: https://doi.org/10.1007/978-94-009-4017-8_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8282-2
Online ISBN: 978-94-009-4017-8
eBook Packages: Springer Book Archive