A criterion for complete reducibility and some applications

Cabanes, Marc

Représentations linéaires des groupes finis - Luminy, 16-21 mai 1988, Astérisque no. 181-182 (1990), p. 93-112

@incollection{AST_1990__181-182__93_0,
     author = {Cabanes, Marc},
     title = {A criterion for complete reducibility and some applications},
     booktitle = {Repr\'esentations lin\'eaires des groupes finis - Luminy, 16-21 mai 1988},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {181-182},
     year = {1990},
     pages = {93-112},
     zbl = {0799.16007},
     mrnumber = {1051244},
     language = {en},
     url = {http://www.numdam.org/item/AST_1990__181-182__93_0}
}

Cabanes, Marc. A criterion for complete reducibility and some applications, in Représentations linéaires des groupes finis - Luminy, 16-21 mai 1988, Astérisque, no. 181-182 (1990), pp. 93-112. http://www.numdam.org/item/AST_1990__181-182__93_0/

References

[1]. H. H. Andersen, Extensions of simple modules for finite Chevalley groups, J. Algebra, 111-2 (1987), 388-403. | Article | MR 916175 | Zbl 0626.20029

[2]. H. H. Andersen, J. Jorgensen and P. Landrock, The projective indecomposable modules of $S L (2, p^{n})$ , Proc. London Math. Soc. (3), 46 (1983), 38-52. | Article | MR 684821 | Zbl 0503.20013

[3]. M. Cabanes, Irreducible modules and Levi supplements, J. Algebra, 90-1 (1984), 84-97. | Article | MR 757083 | Zbl 0548.20027

[4]. M. Cabanes, Brauer morphism between modular Hecke algebras, J. Algebra, 115-1 (1988), 1-31. | Article | MR 937599 | Zbl 0656.20003

[5]. M. Cabanes, Extension groups for modular Hecke algebras, J. Fac. Sci Univ. Tokyo, Sect. IA, 36 (2) (1989), 347-362. | MR 1015003 | Zbl 0727.20006

[6]. R. Carter and G. Lusztig, Modular representations of finite groups of Lie type, Proc. London Math. Soc, (3)32 (1976), 347-384. | Article | MR 396731 | Zbl 0338.20013

[7]. J. A. Green, On a theorem of Sawada, J. London Math. Soc. (2), 18 (1978), 247-252. | Article | MR 509940 | Zbl 0403.16009

[8]. J. E. Humphreys, Non-zero ${Ext}^{1}$ for Chevalley groups (via algebraic groups), J. London Math. Soc. (2) 31 (1985), 463-467. | Article | MR 812774 | Zbl 0567.20029

[9]. J. C. Jantzen, Representations of algebraic groups, Pure and applied mathematics 131, Academic Press, 1987. | MR 899071 | Zbl 0654.20039

[10]. M. A. Ronan and S. D. Smith, Sheaves on buildings and modular representations of Chevalley groups, J. Algebra, 95-2 (1985), 319-347. | Article | MR 810532 | Zbl 0604.20043

[11]. F. Richen, Modular representations of split $(B, N)$ -pairs, Trans. Amer. Math. Soc., 140 (1969), 435-460. | MR 242972 | Zbl 0181.03801

[12]. H. Sawada, A characterization of the modular representations of finite groups with split $(B, N)$ -pairs, Math. Z., 155 (1977), 29-41. | Article | MR 450384 | Zbl 0345.20009

[13]. S. Smith, Irreducible modules and parabolic subgroups, J. Algebra, 75 (1982), 286-289. | Article | MR 650422 | Zbl 0496.20030

[14]. S. Smith, Sheaf homology and complete reducibility, J. Algebra, 95-1 (1985), 72-80. | Article | MR 797655 | Zbl 0609.20026

[15]. R. Steinberg, Representations of algebraic groups, Nagoya Math. J., 22 (1963), 33-56. | Article | MR 155937 | Zbl 0271.20019

[16]. N. Tinberg, Modular representations of finite groups with unsaturated split $(B, N)$ -pairs, Can. J. Math., Vol XXXII (3), (1980), 714-733. | Article | MR 586988 | Zbl 0443.20011

[17]. N. Tinberg, Some indecomposable modules of groups with split $B N$ -pairs, J. Algebra, 61 (1979), 508-526. | Article | MR 559852 | Zbl 0434.20002

[18] M. Auslander, Representation theory of Artin algebras I, Comm. Algebra, 1(3) (1974), 177-268. | Article | MR 349747 | Zbl 0285.16028

[19] H. Völklein, On extensions between simple modules of a Chevalley group, to appear in Proceedings of the Brixen group theory meeting. | MR 1068372 | Zbl 0727.20032