Literature cited
G. D. James, The Representation Theory of the Symmetric Group, Addison-Wesley, Reading (1981).
C. W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Interscience, New York (1962).
D. J. Benson, "Brauer trees for 12M22," J. Algebra,95, No. 2, 398–408 (1985).
R. Carter, Finite Groups of Lie Type. Conjugacy Classes and Complex Characters, Wiley, Chichester (1985).
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of Finite Groups, Clarendon, Oxford (1985).
L. Dornhoff, Group Representation Theory, Part B, Modular Representation Theory, Marcel Dekker, New York (1972).
D. M. Evans, "The 7-modular representations of Janko's smallest simple group," J. Algebra,96, No. 1, 35–44 (1985).
W. Feit, "Blocks with cyclic defect groups for some sporadic groups," Carleton-Ottawa Math. Lect. Note Ser., No. 2, 12/1–12/40 (1984).
P. Fong, "On the decomposition numbers ofT 1 andR(q)," Symp. Math.,13, 415–422 (1972).
R. L. Greiss, "A remark about representations of .1," Commun. Algebra,13, No. 4, 835–844 (1985).
J. E. Humphreys, "Some computations of Cartan invariants for finite groups of Lie type," Commun. Pure Appl. Math.,26, No. 5/6, 745–755 (1973).
J. E. Humphreys, Ordinary and Modular Representations of Chevalley Groups, Lect. Notes Math., Vol. 528, Springer-Verlag, New York (1976).
J. F. Humphreys, "The projective characters of the Mathieu group M12 and of its automorphism group," Math. Proc. Cambridge Phil. Soc.,87, No. 3, 401–412 (1980).
J. F. Humphreys, "The projective characters of the Mathieu group M22," J. Algebra,76, No. 1, 1–24 (1982).
J. F. Humphreys, "The modular characters of the Higman-Sims simple group," Proc. R. Soc. Edinburgh,A92, Nos. 3–4, 319–335 (1982).
G. D. James, "The modular characters of the Mathieu groups," J. Algebra,27, No. 1, 57–111 (1973).
P. Landrock, "The nonprincipal 2-blocks of sporadic simple groups," Commun. Algebra,6, No. 18, 1865–1895 (1978).
L. DiMartino, "Simple linear groups all of whose involutions are 2-reflections," Boll. U. M. I., Ser. 5,15-B, No. 2, 509–526 (1978).
W. Meyer, W. Neutsch, and R. Parker, "The minimal 5-representation of Lyons sporadic group," Math. Ann.,272, No. 1, 29–39 (1985).
R. Steinberg, Endomorphisms of Linear Algebraic Groups, Memoirs of the American Mathematical Society, Vol. 80, Providence (1968).
J. Thackray, Modular Representations of Some Finite Groups, PhD Thesis, Cambridge University (1981).
A. J. Woldar, "On the 5-decomposition matrix for McLaughlin's sporadic simple groups," Commun. Algebra,14, No. 2, 277–291 (1986).
Additional information
Translated from Algebra i Logika, Vol. 27, No. 5, pp. 535–561, September–October, 1988.
Rights and permissions
About this article
Cite this article
Kondrat'ev, A.S. Decomposition numbers of the group . Algebra and Logic 27, 333–349 (1988). https://doi.org/10.1007/BF01982273
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01982273