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Modular representations of reductive groups

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Group Theory, Beijing 1984

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1185))

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References

  1. H.H. Andersen: Cohomology of line bundles on G/B, Ann. Scient. Éc. Norm. Sup. (4) 12 (1979), 85–100

    Article  MathSciNet  MATH  Google Scholar 

  2. H.H. Andersen: The first cohomology group of a line bundle on G/B, Invent. math. 51 (1979), 287–296

    Article  MathSciNet  MATH  Google Scholar 

  3. H.H. Andersen: The strong linkage principle, J. reine angew. Math. 315 (1980), 53–59

    MathSciNet  MATH  Google Scholar 

  4. H.H. Andersen: The Frobenius morphism on the cohomology of homogeneous vector bundles on G/B, Ann. of Math. 112 (1980), 113–121

    Article  MathSciNet  MATH  Google Scholar 

  5. H.H. Andersen: On the structure of Weyl modules, Math. Z. 170 (1980), 1–14

    Article  MathSciNet  MATH  Google Scholar 

  6. H.H. Andersen: On the structure of the cohomology of line bundles on G/B, J. Algebra 71 (1981), 245–258

    Article  MathSciNet  MATH  Google Scholar 

  7. H.H. Andersen: Extensions of modules for algebraic groups, Amer. J. Math. 106 (1984), 489–504

    Article  MathSciNet  MATH  Google Scholar 

  8. H.H. Andersen: An inversion formula for the Kazhdan-Lusztig polynomials for affine Weyl groups, Adv. in Math.

    Google Scholar 

  9. H.H. Andersen: Filtrations of cohomology modules for Chevalley groups, Ann. Scient. Éc. Norm. Sup. (4) 16 (1983), 495–528

    Article  MathSciNet  MATH  Google Scholar 

  10. H.H. Andersen: Schubert varieties and Demazure's character formula

    Google Scholar 

  11. H.H. Andersen, J.C. Jantzen: Cohomology of induced representations for algebraic groups, Math. Ann. 269 (1984), 487–525

    Article  MathSciNet  MATH  Google Scholar 

  12. E. Cline, B. Parshall, L. Scott: Induced modules and affine quotients, Math. Ann. 230 (1977), 1–14

    Article  MathSciNet  MATH  Google Scholar 

  13. E. Cline, B. Parshall, L. Scott: On injective modules for infinitesimal algebraic groups I, Proc. London Math. Soc.

    Google Scholar 

  14. E. Cline, B. Parshall, L. Scott, W. van der Kallen: Rational and generic cohomology, Invent. math. 39 (1977), 143–163

    Article  MathSciNet  MATH  Google Scholar 

  15. S. Donkin: The blocks of a semi-simple algebraic group, J. Algebra 67 (1980), 36–53

    Article  MathSciNet  MATH  Google Scholar 

  16. S. Donkin: Tensor products and filtrations for rational representations of algebraic groups

    Google Scholar 

  17. W. Haboush: Homogeneous vector bundles and reductive subgroups of reductive algebraic groups, Amer. J. Math. 100 (1978), 1123–1137

    Article  MathSciNet  MATH  Google Scholar 

  18. W. Haboush: Central differential operators on split semi-simple groups over fields of positive characteristic, pp. 35–85 in: Séminaire d'Algèbre P. Dubreil et M.-P. Malliavin (Proc. 1979), Lecture Notes in Mathematics 795, Berlin/Heidelberg/New York 1980 (Springer)

    Chapter  Google Scholar 

  19. W. Haboush: A short proof of the Kempf vanishing theorem, Invent. math. 56 (1980), 109–112

    Article  MathSciNet  MATH  Google Scholar 

  20. R. Hartshorne: Algebraic Geometry, New York/Heidelberg/Berlin 1977 (Springer)

    Book  MATH  Google Scholar 

  21. J.E. Humphreys: Modular representations of classical Lie algebras and semisimple groups, J. Algebra 19 (1971), 51–79

    Article  MathSciNet  MATH  Google Scholar 

  22. J.E. Humphreys: Linear Algebraic Groups, Berlin/Heidelberg/New York 1975 (Springer)

    Book  MATH  Google Scholar 

  23. J.E. Humphreys, J.C. Jantzen: Blocks and indecomposable modules for semisimple algebraic groups, J. Algebra 54 (1978), 494–503

    Article  MathSciNet  MATH  Google Scholar 

  24. B. Iversen: The geometry of algebraic groups, Advances in Math. 20 (1976), 57–85

    Article  MathSciNet  MATH  Google Scholar 

  25. J.C. Jantzen: Zur Charakterformel gewisser Darstellungen halbeinfacher Gruppen und Lie-Algebren, Math. Z. 140 (1974), 127–149

    Article  MathSciNet  MATH  Google Scholar 

  26. J.C. Jantzen: Darstellungen halbeinfacher Gruppen und kontravariante Formen, J. reine angew. Math. 290 (1977), 157–199

    MathSciNet  MATH  Google Scholar 

  27. J.C. Jantzen: Über das Dekompositionsverhalten gewisser modularer Darstellungen halbeinfacher Gruppen und ihrer Lie-Algebren, J. Algebra 49 (1977), 441–469

    Article  MathSciNet  MATH  Google Scholar 

  28. J.C. Jantzen: Weyl modules for groups of Lie type, pp. 291–300 in M. Collins (ed.), Finite Simple Groups II (Proc. Durham 1978), London/New York 1980 (Academic Press)

    Google Scholar 

  29. J.C. Jantzen: Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne, J. reine angew. Math. 317 (1980), 157–199

    MathSciNet  MATH  Google Scholar 

  30. V. Kac, B. Weisfeiler: Coadjoint action of a semisimple algebraic group and the center of the enveloping algebra in characteristic p, Indag. math. 38 (1976), 136–151

    Article  MathSciNet  MATH  Google Scholar 

  31. S. Kato: Spherical functions and a q-analogue of Kostant's weight multiplicity formula, Invent. math. 66 (1982), 461–468

    Article  MathSciNet  MATH  Google Scholar 

  32. S. Kato: On the Kazhdan-Lusztig polynomials for affine Weyl groups, Adv. in Math. 55 (1985), 103–130

    Article  MathSciNet  MATH  Google Scholar 

  33. G. Kempf: Linear systems on homogeneous spaces, Ann. of Math. 103 (1976), 557–591

    Article  MathSciNet  MATH  Google Scholar 

  34. G. Kempf: The Grothendieck-Cousin complex of an induced representation, Adv. in Math. 29 (1978), 310–396

    Article  MathSciNet  MATH  Google Scholar 

  35. M. Koppinen: On the composition factors of Weyl modules, Math. Scand. 51 (1982), 212–216

    Article  MathSciNet  MATH  Google Scholar 

  36. M. Koppinen: On the translation functors for a semisimple algebraic group, Math. Scand. 51 (1982), 217–226

    Article  MathSciNet  MATH  Google Scholar 

  37. S. Lang: Algebra (2nd ed.), Reading, Mass. 1984 (Addison-Wesley)

    MATH  Google Scholar 

  38. G. Lusztig: Some problems in the representation theory of finite Chevalley groups, pp. 313–317 in: B. Cooperstein, G. Mason (eds.), The Santa Cruz Conference on Finite Groups (1979), Proc. Symp. Pure Math. 37, Providence, R.I. 1980 (Amer. Math. Soc.)

    Chapter  Google Scholar 

  39. V.B. Mehta, A. Ramanathan: Frobenius splitting and cohomology vanishing for Schubert varieties (to appear)

    Google Scholar 

  40. J. O'Halloran: Cohomology of a Borel subgroup of a Chevelley group (to appear)

    Google Scholar 

  41. S. Ramanan, A. Ramanathan: Projective normality of flag varieties and Schubert varieties, Invent. math. 79 (1985), 217–224

    Article  MathSciNet  MATH  Google Scholar 

  42. C.S. Seshadri: Line bundles on Schubert varieties (to appear)

    Google Scholar 

  43. T.A. Springer: Linear Algebraic Groups, Boston/Basel/Stuttgart 1981 (Birkhäuser)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut der Universität, Wegelerstraße 10, D-5300, Bonn 1, Germany

    J. C. Jantzen

  2. Mathematisches Seminar der Universität, Bundesstr. 55, D-2000, Hamburg 13, Germany

    J. C. Jantzen

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  1. J. C. Jantzen
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Hsio-Fu Tuan

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© 1986 Springer-Verlag

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Jantzen, J.C. (1986). Modular representations of reductive groups. In: Tuan, HF. (eds) Group Theory, Beijing 1984. Lecture Notes in Mathematics, vol 1185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076173

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  • DOI: https://doi.org/10.1007/BFb0076173

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16456-2

  • Online ISBN: 978-3-540-39793-9

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