This is a preview of subscription content, log in via an institution to check access.
Literature Cited
R. Brauer and C. Nesbitt, “On the modular representations of groups of finite order,” Univ. Toronto Studies, Math. Ser., No. 4 (1937).
Ch. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Interscience, New York-London (1962).
A. I. Kostrikin and I. A. Chubarov, Representations of Finite Groups [in Russian], Itogi Nauki i Tekhniki. Algebra, Topologiya, Geometriya, Vol. 23, VINITI, Moscow (1985). pp. 119–195.
R. A. Parker, Modular Character Tables, Cambridge Univ. (1986).
B. Mortimer, “The modular permutation representations of the known doubly transitive groups,” Proc. London Math. Soc.,41, No. 1, 1–20 (1980).
M. W. Liebeck, “Permutation modules for rank 3 symplectic and orthogonal groups,” J. Algebra,92, No. 1, 9–15 (1985).
M. W. Liebeck, “Permutation modules for rank 3 unitary groups,” J. Algebra,88, No. 2, 317–329 (1984).
R. Brauer and C. Nesbitt, “On the modular characters of groups,” Ann. Math.,42, No. 2, 556–590 (1941).
B. Srinivasan, “On the modular characters of the special linear group SL(2, pn),” Proc. London Math. Soc.,14, No. 3, 101–113 (1964).
R. Burkhardt, “Die Zerlegungsmatrizen der Gruppen PSL(2, pf),” J. Algebra,40, No. 1, 75–96 (1976).
R. Burkhardt, “Über die Zerlegungszahlen der Suzukigruppen Sz(q),” J. Algebra,59, No. 2, 421–433 (1979).
R. Burkhardt, “Über die Zerlegungszahlen der unitären Gruppen PSU(3,22f),” J. Algebra,61, No. 2, 548–581 (1979).
J. Humphreys, “Ordinary and modular characters of SL(3, p),” J. Algebra,72, No. 1, 8–16 (1981).
J. Humphreys, “Cartan invariants,” Bull. London Math. Soc.,17, 1–14 (1985).
P. Bhattacharya, “On the structure of the group ring of an elementary Abelian group and a theorem of Brauer and Nesbitt,” Bull. Class. Sci. Acad. Roy. Belg.,67, No. 4, 260–267 (1981).
A. E. Zalesskii and I. D. Suprunenko, “Reduced symmetric powers of natural realizations of the groups SLm(P) and Spm(P) and their restrictions to subgroups,” Sib. Mat. Zh.,31, No. 4, 33–46 (1990).
C. W. Curtis, N. Iwahori, and R. Kilmoyer, “Hecke algebras and characters of parabolic type of finite groups with (B, N)-pairs,” Publ. Math. IHES,40, 81–116 (1972).
G. Seitz, “Cross characteristic embeddings of finite groups of Lie type,” Preprint, Univ. Oregon (1987).
R. Steinberg, Lectures on Chevalley Groups, Yale University (1967).
M. I. Isaacs, Character Theory of Finite Groups, New York, Academic Press (1976).
A. M. Adamovich, “An analog of the space of primitive forms over a field of positive characteristic,” Vestn. Moscow State University, Ser. 1, Matematika, Mekhanika, No. 1, 64–66 (1984).
B. Huppert, “Singer-Zyklen in klassischen Gruppen,” Math. Z.,117, 141–150 (1970).
C. W. Curtis, W. M. Kantor, and G. M. Seitz, “The 2-transitive permutation representations of the finite Chevalley groups,” Trans. Amer. Math. Soc.,218, 1–59 (1976).
P. Gérardin, “Weil representations associated to finite fields,” J. Algebra,46, 54–101 (1977).
Additional information
Minsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 5, pp. 46–60, September–October, 1990.
Rights and permissions
About this article
Cite this article
Zalesskii, A.E., Suprunenko, I.D. Permutation representations and a fragment of the decomposition matrix of symplectic and special linear groups over a finite field. Sib Math J 31, 744–755 (1990). https://doi.org/10.1007/BF00974487
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00974487