Projective modules for finite Chevalley groups
HTML articles powered by AMS MathViewer
- by John W. Ballard
- Trans. Amer. Math. Soc. 245 (1978), 221-249
- DOI: https://doi.org/10.1090/S0002-9947-1978-0511407-9
- PDF | Request permission
Abstract:
The purpose of this paper is to obtain character formulas for certain indecomposable projective modules for a finite Chevalley group. It is shown that these modules are also modules for the corresponding semisimple algebraic group.References
- John W. Ballard, Some generalized characters of finite Chevalley groups, Math. Z. 147 (1976), no. 2, 163–174. MR 399280, DOI 10.1007/BF01164280
- N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
- Richard Brauer, A characterization of the characters of groups of finite order, Ann. of Math. (2) 57 (1953), 357–377. MR 53942, DOI 10.2307/1969864
- Charles W. Curtis, Representations of Lie algebras of classical type with applications to linear groups, J. Math. Mech. 9 (1960), 307–326. MR 0110766, DOI 10.1512/iumj.1960.9.59018
- Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0144979
- Harish-Chandra, Lie algebras and the Tannaka duality theorem, Ann. of Math. (2) 51 (1950), 299–330. MR 33811, DOI 10.2307/1969326
- J. E. Humphreys, Modular representations of classical Lie algebras and semisimple groups, J. Algebra 19 (1971), 51–79. MR 283038, DOI 10.1016/0021-8693(71)90115-3
- James E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1972. MR 0323842, DOI 10.1007/978-1-4612-6398-2
- J. E. Humphreys, Projective modules for $\textrm {SL}(2,$ $q)$, J. Algebra 25 (1973), 513–518. MR 399241, DOI 10.1016/0021-8693(73)90097-5
- J. E. Humphreys and D. N. Verma, Projective modules for finite Chevalley groups, Bull. Amer. Math. Soc. 79 (1973), 467–468. MR 320176, DOI 10.1090/S0002-9904-1973-13220-3
- Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
- G. Lusztig, Divisibility of projective modules of finite Chevalley groups by the Steinberg module, Bull. London Math. Soc. 8 (1976), no. 2, 130–134. MR 401900, DOI 10.1112/blms/8.2.130
- Bhama Srinivasan, On the Steinberg character of a finite simple group of Lie type, J. Austral. Math. Soc. 12 (1971), 1–14. MR 0291317, DOI 10.1017/S1446788700008247
- Robert Steinberg, Representations of algebraic groups, Nagoya Math. J. 22 (1963), 33–56. MR 155937, DOI 10.1017/S0027763000011016 —, Lectures on Chevalley groups, Yale Univ. Lecture Notes, 1967.
- Robert Steinberg, Endomorphisms of linear algebraic groups, Memoirs of the American Mathematical Society, No. 80, American Mathematical Society, Providence, R.I., 1968. MR 0230728
- Daya-Nand Verma, The rôle of affine Weyl groups in the representation theory of algebraic Chevalley groups and their Lie algebras, Lie groups and their representations (Proc. Summer School, Bolyai János Math. Soc., Budapest, 1971) Halsted, New York, 1975, pp. 653–705. MR 0409673
- W. J. Wong, Representations of Chevalley groups in characteristic $p$, Nagoya Math. J. 45 (1972), 39–78. MR 302776, DOI 10.1017/S0027763000014653
- W. J. Wong, Irreducible modular representations of finite Chevalley groups, J. Algebra 20 (1972), 355–367. MR 299700, DOI 10.1016/0021-8693(72)90063-4
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 245 (1978), 221-249
- MSC: Primary 20C20; Secondary 20G05
- DOI: https://doi.org/10.1090/S0002-9947-1978-0511407-9
- MathSciNet review: 511407