Loewy series of certain indecomposable modules for Frobenius subgroups
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- by Zong Zhu Lin PDF
- Trans. Amer. Math. Soc. 332 (1992), 391-409 Request permission
Abstract:
We imitate some approaches in infinite dimensional representation theory of complex semisimple Lie algebras by using the truncated category method in the categories of modules for certain Frobenius subgroups of a semisimple algebraic group over an algebraically closed field of characteristic $p > 0$. By studying the translation functors from $p$-singular weights to $p$-regular weights, we obtain some results on Loewy series of certain indecomposable modules.References
- Henning Haahr Andersen, An inversion formula for the Kazhdan-Lusztig polynomials for affine Weyl groups, Adv. in Math. 60 (1986), no. 2, 125–153. MR 840301, DOI 10.1016/S0001-8708(86)80008-1
- Henning Haahr Andersen and Masaharu Kaneda, Loewy series of modules for the first Frobenius kernel in a reductive algebraic group, Proc. London Math. Soc. (3) 59 (1989), no. 1, 74–98. MR 997252, DOI 10.1112/plms/s3-59.1.74
- E. Cline, B. Parshall, and L. Scott, Algebraic stratification in representation categories, J. Algebra 117 (1988), no. 2, 504–521. MR 957457, DOI 10.1016/0021-8693(88)90123-8
- Edward T. Cline, Brian J. Parshall, and Leonard L. Scott, Duality in highest weight categories, Classical groups and related topics (Beijing, 1987) Contemp. Math., vol. 82, Amer. Math. Soc., Providence, RI, 1989, pp. 7–22. MR 982273, DOI 10.1090/conm/082/982273
- Stephen Donkin, Rational representations of algebraic groups, Lecture Notes in Mathematics, vol. 1140, Springer-Verlag, Berlin, 1985. Tensor products and filtration. MR 804233, DOI 10.1007/BFb0074637
- Stephen Donkin, Skew modules for reductive groups, J. Algebra 113 (1988), no. 2, 465–479. MR 929773, DOI 10.1016/0021-8693(88)90172-X
- Stephen Doty, Character formulas and Frobenius subgroups of algebraic groups, J. Algebra 125 (1989), no. 2, 331–347. MR 1018950, DOI 10.1016/0021-8693(89)90169-5
- Thomas J. Enright and Brad Shelton, Categories of highest weight modules: applications to classical Hermitian symmetric pairs, Mem. Amer. Math. Soc. 67 (1987), no. 367, iv+94. MR 888703, DOI 10.1090/memo/0367
- Ronald S. Irving, Projective modules in the category ${\scr O}_S$: Loewy series, Trans. Amer. Math. Soc. 291 (1985), no. 2, 733–754. MR 800260, DOI 10.1090/S0002-9947-1985-0800260-5
- Ronald S. Irving, The socle filtration of a Verma module, Ann. Sci. École Norm. Sup. (4) 21 (1988), no. 1, 47–65. MR 944101 —, Loewy filtrations of Weyl modules, Trans. Amer. Math. Soc. (to appear).
- Ronald S. Irving, Singular blocks of the category $\scr O$, Math. Z. 204 (1990), no. 2, 209–224. MR 1055986, DOI 10.1007/BF02570868
- Jens Carsten Jantzen, Representations of algebraic groups, Pure and Applied Mathematics, vol. 131, Academic Press, Inc., Boston, MA, 1987. MR 899071
- Masaharu Kaneda, Extensions of modules for infinitesimal algebraic groups, J. Algebra 122 (1989), no. 1, 188–210. MR 994943, DOI 10.1016/0021-8693(89)90245-7
- M. Koppinen, On the composition factors of Weyl modules, Math. Scand. 51 (1982), no. 2, 212–216 (1983). MR 690526, DOI 10.7146/math.scand.a-11975
- M. Koppinen, Homomorphisms between neighbouring Weyl modules, J. Algebra 103 (1986), no. 1, 302–319. MR 860709, DOI 10.1016/0021-8693(86)90189-4 Z. Lin, The structure of cohomology of line bundles on the flag varieties for some groups of rank $2$, Ph. D. Thesis, Univ. of Massachusetts, 1989. —, Extensions between simple modules for Frobenius kernels, J. Pure Appl. Algebra 72 (1991), 275-294.
- Horst Schubert, Categories, Springer-Verlag, New York-Heidelberg, 1972. Translated from the German by Eva Gray. MR 0349793
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 332 (1992), 391-409
- MSC: Primary 20G05; Secondary 20G10
- DOI: https://doi.org/10.1090/S0002-9947-1992-1052908-4
- MathSciNet review: 1052908