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A vanishing theorem in relative Lie algebra cohomology

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Algebraic Groups Utrecht 1986

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1271))

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References

  1. W. Baily and A. Borel, Compactifications of arithmetic quotients of bounded symmetric domains, Ann. Math., 84, 1966, p. 442–528.

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Borel, L2-cohomology and intersection cohomology of certain arithmetic varieties, in E. Noether in Bryn Mawr, Springer, 1983, p. 119–131.

    Google Scholar 

  3. A. Borel and W. Casselman, L2-cohomology of locally symmetric manifolds of finite volume, Duke Math. J. 50 (1983), p. 625–647.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Borel et W. Casselman, Cohomologie d'intersection et L2-cohomologie de variétés arithmétiques de rang rationnel 2. C. R. Acad. Sci. Paris 301, (1985), p. 369–373.

    MathSciNet  MATH  Google Scholar 

  5. W. Casselman, L2-cohomology for groups of real rank one, in Representation theory of reductive groups, Progress in Math., 40, Birkhäuser, Boston, 1983, p. 69–82.

    Google Scholar 

  6. T. Enright, Relative Lie algebra cohomology and unitary representations of complex Lie groups, Duke Math. J. 47, (1980), p. 1–15.

    Article  MathSciNet  Google Scholar 

  7. S. Helgason, Differential Geometry and Symmetric Spaces, Adademic Press 1962.

    Google Scholar 

  8. B. Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Annals of Math. 74, (1961), p. 329–387.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Tits, Classification of algebraic semisimple groups, in Algebraic groups and discontinuous subgroups, Proc. Symp. Pure Math. A.M.S. IX, (1966), p. 33–62.

    Article  MathSciNet  MATH  Google Scholar 

  10. D. Vogan, Unitarizability of certain series of representations, Annals of Math., 120, (1984), p. 141–187.

    Article  MathSciNet  MATH  Google Scholar 

  11. D. Vogan and G. Zuckerman, Unitary representations with non-zero cohomology, Comp. Math., 53, 1984, p. 51–90.

    MathSciNet  MATH  Google Scholar 

  12. S. Zucker, L2-cohomology and intersection homology of locally symmetric varieties II, preprint, 1984.

    Google Scholar 

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Arjeh M. Cohen Wim H. Hesselink Wilberd L. J. van der Kallen Jan R. Strooker

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To T. A. Springer, on his 60th anniversary

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© 1987 Springer-Verlag

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Borel, A. (1987). A vanishing theorem in relative Lie algebra cohomology. In: Cohen, A.M., Hesselink, W.H., van der Kallen, W.L.J., Strooker, J.R. (eds) Algebraic Groups Utrecht 1986. Lecture Notes in Mathematics, vol 1271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079230

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  • DOI: https://doi.org/10.1007/BFb0079230

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18234-4

  • Online ISBN: 978-3-540-47834-8

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