Dimensional criteria for semisimplicity of representations

Proceedings of the London Mathematical Society

Volumn 76, Issue 1, 1998, Pages 95-149

  McNinch, George J ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

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[No Author keywords available]

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EID: 0002558673     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024611598000045     Document Type: Article

References (26)

1. H. H. ANDERSEN and J. C. JANTZEN, 'Cohomology of induced representations for algebraic groups', Math. Ann. 269 (1984) 487-525.
2. A. BOREL, Linear algebraic groups, 2nd edn, Graduate Texts in Mathematics 129 (Springer, Berlin, 1991).
3. N. BOURBAKI, Groupes et algèbres de Lie (Hermann, Paris, 1968).
4. C. W. CURTIS and I. REINER, Methods of representation theory, vol. 1 (Wiley-Interscience, New York, 1981).
5. S. DONKIN, Rational representations of algebraic groups: tensor products and filtrations, Lecture Notes in Mathematics 1140 (Springer. Berlin, 1985).
6. S. DONKIN, 'On tilting modules for algebraic groups', Math. Z. 212 (1993) 39-60.
7. P. G. GILKEY and G. M. SEITZ, 'Some representations of exceptional Lie algebras', Geom. Dedicata 25 (1988) 407-416.
8. J. HUMPHREYS, An introduction to Lie algebras and representation theory, 3rd edn, Graduate Texts in Mathematics 9 (Springer, Berlin, 1980).
9. J. C. JANTZEN, Darstellungen halbeinfacher algebraischer Gruppen und zugeordnete kontravariante Formen, Bonner Mathematische Schriften 67 (Universität Bonn, 1973).
10. J. C. JANTZEN, Representations of algebraic groups, Pure and Applied Mathematics 131 (Academic Press, Orlando, FL, 1987).
11. J. C JANTZEN, 'First cohomology groups for classical Lie algebras'. Representation theory of finite groups and finite dimensional algebras (Bielefeld) (eds G. O. Michler and C. M. Ringel), Progress in Mathematics 95 (Birkhäuser, Basel, 1991), pp. 289-315.
12. J. C. JANTZEN, 'Low dimensional representations of reductive groups are semisimple', Algebraic groups and related subjects; a volume in honour of R. W. Richardson (eds G. Lehrer et al., Cambridge University Press, 1996).
13. P. KLEIDMAN and M. LIEBECK, The subgroup structure of the finite classical groups, London Mathematical Society Lecture Notes Series 129 (Cambridge University Press, London, 1990).
14. M. LARSEN, 'On the semisimplicity of low-dimensional representations of semisimple groups in characteristic p', J. Algebra 173 (1995) 219-236.
15. M. MALIAKIS, 'The universal form of the branching rule for the symplectic groups', J. Algebra 168 (1994) 221-248.
16. O. MATHIEU, 'Filiations of G-modules', Ann. Sci. École Norm. Sup. 23 (1990) 625-644.
17. A. A. PREMET, 'Weights of infinitesimally irreducible representations of Chevalley groups over a field of prime characteristic', Math. USSR Sb. 61 (1988) 167-183.
18. A. A. PREMET and I. D. SUPRUNENKO, 'The Weyl modules and the irreducible representations of the symplectic group with the fundamental highest weights', Comm. Algebra 11 (1983) 1309-1342.
19. C. M. RINGEL, 'The category of modules with good fillrations over a quasi-hereditary algebra has almost split sequences', Math. Z. 208 (1991) 209-223.
20. G. M. SEITZ, Maximal subgroups of classical algebraic groups, Memoirs of the American Mathematical Society 365 (American Mathematical Society, Providence, R. I., 1987).
21. G. M. SEITZ, 'Abstract homomorphisms of algebraic groups', J. London Math Soc. (2) 56 (1997) 104-124.
22. J.-P. SERRE, 'Sur la semi-simplicité des produits tensoriels de représentations de groupes', Invent. Math. 116 (1994) 513-530.
23. T. A. SPRINGER, 'Weyl's character formula for algebraic groups', Invent. Math 5 (1968) 85-105.
24. R. STEINBERG, Lectures on Chevalley groups (Yale University, 1968).
25. ℓ with bounded higher weights in reduction modulo p' (in Russian), Vestsĩ Akad. Navuk BSSR, Ser. Fīz.-Mat. Navuk (1983) no. 2, 18-22.
26. V. S. VARADARAJAN, Lie groups, Lie algebras, and their representations, Graduate Texts in Mathematics 102 (Springer, Berlin, 1974).