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Variations on a theme of Steinberg. (English) Zbl 1054.20026
The paper extends the Steinberg tensor product theorem (which is important in the representation theory of simple algebraic groups over fields of positive characteristic) from the target group \(\text{SL}(V)\) to an arbitrary simple algebraic group.

MSC:
20G05 Representation theory for linear algebraic groups
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[1] Andersen, H.H; Jorgensen, J; Landrock, P, The projective indecomposable modules of SL(2,pn), Proc. London math. soc., 46, 495-528, (1983)
[2] Burgoyne, N; Williamson, C, Some computations involving simple Lie algebras, (), 162-171
[3] Jantzen, J.C, Representations of algebraic groups, (1987), Academic Press · Zbl 0652.20042
[4] Lawther, R, Jordan block sizes of unipotent elements in exceptional algebraic groups, Comm. algebra, 23, 4125-4156, (1995) · Zbl 0880.20034
[5] Lawther, R; Testerman, D, A1 subgroups of exceptional algebraic groups, Mem. amer. math. soc., 674, 1-131, (1999) · Zbl 0936.20039
[6] Liebeck, M.W; Seitz, G.M, Subgroups generated by root elements in groups of Lie type, Ann. of math., 139, 293-361, (1994) · Zbl 0824.20041
[7] Liebeck, M.W; Seitz, G.M, Reductive subgroups of exceptional algebraic groups, Mem. amer. math. soc., 121, 580, (1996) · Zbl 0851.20045
[8] Liebeck, M.W; Seitz, G.M, On the subgroup structure of classical groups, Invent. math., 134, 427-453, (1998) · Zbl 0920.20039
[9] Liebeck, M.W; Seitz, G.M, On the subgroup structure of exceptional groups of Lie type, Trans. amer. math. soc., 350, 3409-3482, (1998) · Zbl 0905.20031
[10] M.W. Liebeck, G.M. Seitz, The maximal subgroups of positive dimension in exceptional algebraic groups, to appear · Zbl 1058.20040
[11] McNinch, G.J, Dimensional criteria for semisimplicity of representations, Proc. London math. soc., 76, 95-149, (1998)
[12] Seitz, G.M, Maximal subgroups of exceptional algebraic groups, Mem. amer. math. soc., 90, 441, (1991) · Zbl 0743.20029
[13] Seitz, G.M, Unipotent elements, tilting modules, and saturation, Invent. math., 141, 467-502, (2000) · Zbl 1053.20043
[14] Steinberg, R, Representations of algebraic groups, Nagoya math. J., 22, 33-56, (1963) · Zbl 0271.20019
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