Jantzen, Jens Carsten Zur Reduktion modulo p unipotenter Charaktere endlicher Chevalley- Gruppen. (German) Zbl 0502.20022 Math. Z. 181, 97-128 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 5 Documents MSC: 20G05 Representation theory for linear algebraic groups 20C20 Modular representations and characters 20G40 Linear algebraic groups over finite fields 14F20 Étale and other Grothendieck topologies and (co)homologies 14L17 Affine algebraic groups, hyperalgebra constructions Keywords:reductions modulo p; Deligne-Lusztig characters; finite Chevalley groups; characters of Weyl modules; unipotent representations; irreducible p- modular representations; simply connected simple algebraic group; maximal torus; character group; Weyl group; Dynkin diagram; Frobenius morphism; twisted group; virtual character; fundamental weights; irreducible module; projective module; hyperalgebra; infinitesimal subgroup; primitive ideals; enveloping algebra; complex simple Lie algebra; Brauer character Citations:Zbl 0477.20024 PDFBibTeX XMLCite \textit{J. C. Jantzen}, Math. Z. 181, 97--128 (1982; Zbl 0502.20022) Full Text: DOI EuDML References: [1] Barbasch, D., Vogan, D.: Primitive ideals and orbital integrals in complex classical groups. Math. Ann.259, 153-199 (1982) · Zbl 0489.22010 [2] Bourbaki, N.: Algèbre commutative. Chapitres 5 et 6. Paris: Hermann 1964 · Zbl 0205.34302 [3] Bourbaki, N.: Groupes et algèbres de Lie. Chapitres 4, 5 et 6. Paris: Hermann 1968 · Zbl 0186.33001 [4] Brylinski, J.L., Kashiwara, M.: Kazhdan-Lusztig conjecture and holonomic systems. Invent. Math.64, 387-410 (1981) · Zbl 0473.22009 [5] Deligne, P., Lusztig, G.: Representations of reductive groups over finite fields. Ann. of Math. (2)103, 103-161 (1976) · Zbl 0336.20029 [6] Feit, W.: Characters of finite groups. New York-Amsterdam: Benjamin 1967 · Zbl 0166.29002 [7] James, G.D.: The representation theory of the symmetric groups. Lecture Notes in Mathematics682. Berlin-Heidelberg-New York: Springer 1978 [8] Jantzen, J.C.: Über das Dekompositionsverhalten gewisser modularer Darstellungen halbeinfacher Gruppen und ihrer Lie-Algebren. J. Algebra49, 441-469 (1977) · Zbl 0386.20018 [9] Jantzen, J.C.: Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne. J. Reine Angew. Math.317, 157-199 (1980) · Zbl 0451.20040 [10] Jantzen, J.C.: Moduln mit einem höchsten Gewicht. Lectures Notes in Mathematics750. Berlin-Heidelberg-New York: Springer 1979 · Zbl 0426.17001 [11] Jantzen, J.C.: Zur Reduktion modulop der Charaktere von Deligne und Lusztig. J. Algebra70, 452-474 (1981) · Zbl 0477.20024 [12] Joseph, A.:W-module structure in the primitive spectrum of the enveloping algebra of a semisimple Lie algebra. In: Non-commutative harmonic analysis (ed.: J. Carmona, M. Vergne). Actes d’un Colloque (Marseille 1978), pp. 116-135. Lecture Notes in Mathematics728. Berlin-Heidelberg-New York: Springer 1979 [13] Kazhdan, D., Lusztig, G.: Representations of Coxeter groups and Hecke algebras. Invent. Math.53, 165-184 (1979) · Zbl 0499.20035 [14] Lusztig, G.: Hecke algebras and Jantzen’s generic decomposition patterns. Advances in Math.37, 121-164 (1980) · Zbl 0448.20039 [15] Lusztig, G.: Some problems in the representation theory of finite Chevalley groups. In: The Santa Cruz Conference on Finite Groups (Santa Cruz 1979), pp. 313-317. Proceedings of Symposia in Pure Mathematics37. Providence, Rhode Island: Amer. Math. Soc. 1980 [16] Lusztig, G.: On the unipotent characters of the exceptional groups over finite fields. Preprint · Zbl 0443.20036 [17] Lusztig, G.: Unipotent characters of the symplectic and odd orthogonal groups over a finite field. Invent. Math.64, 263-296 (1981) · Zbl 0477.20023 [18] Lusztig, G., Srinivasan, B.: The characters of the finite unitary groups. J. Algebra49, 167-171 (1977) · Zbl 0384.20008 [19] Mayer, S.J.: On the characters of the Weyl group of type C. J. Algebra33, 59-67 (1975) · Zbl 0296.20004 [20] Springer, T.A.: A construction of representations of Weyl groups. Invent. Math.44, 279-293 (1978) · Zbl 0376.17002 [21] Frame, J.S.: Group decomposition by double coset matrices. Bull. Amer. Math. Soc.54, 740-755 (1948) · Zbl 0032.10501 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.