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Complex manifolds and unitary representations

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Part of the Lecture Notes in Mathematics book series (LNM,volume 185)

Keywords

  • Unitary Representation
  • Parabolic Subgroup
  • Series Representation
  • Closed Orbit
  • Maximal Compact Subgroup

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References

  1. A. Andreotti and E. Vesentini, Carleman estimates for the Laplace-Beltrami operator on complex manifolds, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 81–130.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. R. Bott, Homogeneous vector bundles, Ann. of Math. (2) 66 (1957), 203–248.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. F. Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France 84 (1956), 97–205.

    MathSciNet  MATH  Google Scholar 

  4. J. M. G. Fell, book on harmonic analysis, in preparation.

    Google Scholar 

  5. Harish-Chandra, Representations of a semisimple Lie group on a Banach space, I, Trans. Amer. Math. Soc. 75 (1953), 185–243.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. —, The Plancherel formula for complex semisimple Lie groups, Trans. Amer. Math. Soc. 76 (1954), 485–528.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. —, Representations of semisimple Lie groups, IV, Amer. J. Math. 77 (1955), 743–777; V, ibid. 78 (1956), 1–41; VI, ibid. 78 (1956), 564–628.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. —, Discrete series for semisimple Lie groups, II, Acta Math. 116 (1966), 1–111.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. —, Harmonic analysis on semisimple Lie groups, Bull. Amer. Math. Soc. 76 (1970), 529–551.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. S. Helgason, Applications of the Radon transform to representations of semisimple Lie groups, Proc. Nat. Acad. Sci. U. S. A. 63 (1969), 643–647.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. —, A duality for symmetric spaces with applications to group representations, to appear.

    Google Scholar 

  12. A. W. Knapp and E. M. Stein, Singular integrals and the principal series, Proc. Nat. Acad. Sci. U. S. A. 63 (1969), 281–284; II, ibid., to appear.

    CrossRef  MATH  Google Scholar 

  13. B. Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math. (2) 74 (1961), 329–387.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. —, On the existence and irreducibility of certain series of representations, Bull. Amer. Math. Soc. 75 (1969), 627–642.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. R. A. Kunze and E. M. Stein, Uniformly bounded representations, III, Amer. J. Math. 89 (1967), 385–442.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. M. S. Narasimhan and K. Okamoto, An analogue of the Borel-Weil-Bott theorem for hermitian symmetric pairs of noncompact type, Ann. of Math. (2) 91 (1970), 486–511.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. K. R. Parthasarathy, R. Ranga-Rao and V. S. Varadarajan, Representations of complex semisimple Lie groups and Lie algebras, Ann. of Math. (2) 85 (1967), 383–429.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. W. Schmid, On a conjecture of Langlands, Ann. of Math., 1970.

    Google Scholar 

  19. N. R. Wallach, Cyclic vectors and irreducibility for principal series representations, to appear.

    Google Scholar 

  20. Garth Warner, Harmonic analysis on semisimple Lie groups, Springer-Verlag, Berlin-Heidelberg-New York, to appear about 1971.

    Google Scholar 

  21. J. A. Wolf, The action of a real semisimple group on a complex flag manifold. I: Orbit structure and holomorphic arc components, Bull. Amer. Math. Soc. 75 (1969), 1121–1237.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. —, II: Unitary representations on partially holomorphic cohomology spaces, to appear.

    Google Scholar 

  23. —, III: Induced representations based on hermitian symmetric spaces, in preparation.

    Google Scholar 

  24. D. P. Zelobenko, Analysis of irreducibility in the class of elementary representations of a complex semisimple Lie group, Math. USSR-Izv. 2 (1968), 105–128.

    CrossRef  Google Scholar 

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© 1971 Springer-Verlag

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Wolf, J.A. (1971). Complex manifolds and unitary representations. In: Horváth, J. (eds) Several Complex Variables II Maryland 1970. Lecture Notes in Mathematics, vol 185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058772

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  • DOI: https://doi.org/10.1007/BFb0058772

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05372-9

  • Online ISBN: 978-3-540-36493-1

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