Skip to main content

Recent developments in representation theory

  • Überblicksvorträge
  • Conference paper
  • First Online:
Arbeitstagung Bonn 1984

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1111))

Supported in part by NSF grant DMS 8317436.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 19.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 29.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. Angelopolos: Sur les représentations de SŌo (p, 2). C.R. Acad. Sci. Paris 292 (1981), 469–471

    Google Scholar 

  2. J. Arthur: On some problems suggested by the trace formula. In Lie Group Representations II. Springer Lecture Notes in Mathematics 1041 (1984), pp. 1–49

    Article  MathSciNet  MATH  Google Scholar 

  3. M. F. Atiyah and W. Schmid: A geometric construction of the discrete series for semisimple Lie groups. Inventiones Math. 42 (1977), 1–62

    Article  MathSciNet  MATH  Google Scholar 

  4. M. W. Baldoni-Silva: The unitary dual of Sp(n, 1), n≥2. Duke Math. J. 48 (1981), 549–584

    Article  MathSciNet  MATH  Google Scholar 

  5. W. Bargman: Irreducible unitary representations of the Lorentz group. Ann. of Math. 48 (1947), 568–640

    Article  MathSciNet  Google Scholar 

  6. A. Beilinson and J. Bernstein: Localisation de g-modules. C.R. Acad. Sci. Paris, 292 (1981), 15–18

    MathSciNet  MATH  Google Scholar 

  7. J. Bernstein, I. M. Gelfand and S. I. Gelfand: Differential operators on the base affine space and a study of g-modules. In Lie Groups and their Representations. Akadémiai Kiadó, Budapest 1975

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. J.-L. Brylinski and M. Kashiwara: Kazhdan-Lusztig conjectures and holonomic systems. Inventiones Math. 64 (1981), 387–410

    Article  MathSciNet  MATH  Google Scholar 

  10. W. Casselman: Jacquet modules for real reductive groups. In Proceedings of the International Congress of Mathematicians. Helsinki 1978, pp. 557–563

    Google Scholar 

  11. W. Casselman and D. Miličić: Asymptotic behavior of matrix coefficients of admissible representations. Duke Math. J. 49 (1982), 869–930

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Dixmier: Les C*-algèbres et Leur Représentations. Gauthier-Villars, Paris 1964

    MATH  Google Scholar 

  13. M. Duflo: Construction de représentations unitaires d’un groupe de Lie. Preprint

    Google Scholar 

  14. T. J. Enright, R. Howe and N. R. Wallach: A classification of unitary highest weight modules. In Representation Theory of Reductive Groups. Progress in Mathematics 40 (1983), pp. 97–144

    Article  MathSciNet  MATH  Google Scholar 

  15. T. J. Enright, R. Parthasarathy, N. R. Wallach and J. A. Wolf: Unitary derived functor modules with small spectrum. Preprint

    Google Scholar 

  16. M. Flensted-Jensen: Discrete series for semisimple symmetric spaces. Ann. of Math. 111 (1980), 253–311

    Article  MathSciNet  MATH  Google Scholar 

  17. L. Gårding: Note on continuous representations of Lie groups. Proc. Nat. Acad. Sci. USA 33 (1947), 331–332

    Article  MathSciNet  Google Scholar 

  18. Harish-Chandra: Plancherel formula for the 2×2 real unimodular group. Proc. nat. Acad. Sci. USA 38 (1952), 337–342

    Article  MathSciNet  MATH  Google Scholar 

  19. Harish-Chandra: Representations of semisimple Lie groups I. Trans. Amer. Math. Soc. 75 (1953), 185–243

    Article  MathSciNet  MATH  Google Scholar 

  20. Harish-Chandra: The characters of semisimple Lie groups. Trans. Amer. Math. Soc. 83 (1956), 98–163

    Article  MathSciNet  MATH  Google Scholar 

  21. Harish-Chandra: Discrete series for semisimple Lie groups II. Acta Math. 116 (1966), 1–111

    Article  MathSciNet  MATH  Google Scholar 

  22. Harish-Chandra: Harmonic analysis on real reductive groups III. Ann. of Math. 104 (1976), 117–201

    Article  MathSciNet  MATH  Google Scholar 

  23. H. Hecht, D. Miličić, W. Schmid and J. Wolf: Localization of Harish-Chandra modules and the derived functor construction. To appear

    Google Scholar 

  24. H. Hecht and W. Schmid: Characters, asymptotics, and n-homology of Harish-Chandra modules. Acta Math. 151 (1983), 49–151

    Article  MathSciNet  MATH  Google Scholar 

  25. R. Herb: Discrete series characters and Fourier inversion on semisimple real Lie groups. Trans. Amer. Math. Soc. 277 (1983), 241–261

    Article  MathSciNet  MATH  Google Scholar 

  26. R. Herb and J. Wolf: The Plancherel theorem for general semisimple Lie groups. Preprint

    Google Scholar 

  27. T. Hirai: On irreducible representations of the Lorentz groups of n-th order. Proc. Japan. Acad. 38 (1962), 83–87

    Article  MathSciNet  MATH  Google Scholar 

  28. R. Howe: Small unitary representations of classical groups. To appear in the Proceedings of the Mackey Conference, Berkeley 1984

    Google Scholar 

  29. D. Kazhdan and G. Lustzig: Representations of Coxeter groups and Hecke algebras. Inventiones Math. 53 (1979) 165–184

    Article  MathSciNet  MATH  Google Scholar 

  30. A. Knapp and B. Speh: Status of classification of irreducible unitary representations. In Harmonic Analysis, Proceedings, 1981. Springer Lecture Notes in Mathematics 908 (1982), pp. 1–38

    MathSciNet  MATH  Google Scholar 

  31. A. Knapp and G. Zuckerman: Classification of irreducible tempered representations of semisimple groups. Ann. of Math. 116 (1982), 389–501

    Article  MathSciNet  MATH  Google Scholar 

  32. H. Kraljević: Representations of the universal covering group of the group SU(n,1). Glasnik Mat. 8 (1973), 23–72

    MATH  Google Scholar 

  33. R. Langlands: On the classification of irreducible representations of real algebraic groups. Mimeographed notes, Institute for Advanced Study 1973

    Google Scholar 

  34. R. Langlands: On the Functional Equations Satified by Eisenstein series. Springer Lecture Notes in Mathematics 544 (1976)

    Google Scholar 

  35. G. Lusztig and D. Vogan: Singularities of closures of K orbits on flag manifolds. Inventiones Math. 71 (1983)

    Google Scholar 

  36. T. Matsuki: The orbits of affine symmetric spaces under the action of minimal parabolic subgroups. M. Math. Soc. Japan 31 (1979), 331–357

    Article  MathSciNet  MATH  Google Scholar 

  37. T. Matsuki: Closure relation for K-orbits on complex flag manifolds. Preprint

    Google Scholar 

  38. D. Miličić: Asymptotic behavior of matrix coefficients of the discrete series. Duke Math. J. 44 (1977), 59–88

    Article  MathSciNet  MATH  Google Scholar 

  39. E. Nelson: Analytic vectors. Ann. of Math. 70 (1959), 572–615

    Article  MathSciNet  MATH  Google Scholar 

  40. T. Oshima and T. Matsuki: A description of discrete series for semisimple symmetric spaces. To appear in Adv. Studies in Math.

    Google Scholar 

  41. S. J. Prichepionok: A natural topology for linear representations of semisimple Lie algebras. Soviet Math. Dokl. 17 (1976), 1564–66

    Google Scholar 

  42. J. Rawnsley, W. Schmid and J. A. Wolf: Singular unitary representations and indefinite harmonic theory. J. Funct. Anal. 51 (1983), 1–114

    Article  MathSciNet  MATH  Google Scholar 

  43. W. Schmid: Homogeneous complex manifolds and representations of semisimple Lie groups. Thesis, UC Berkeley 1967

    Google Scholar 

  44. W. Schmid: L2-cohomology and the discrete series. Ann. of Math. 102 (1975), 535–564

    Article  MathSciNet  Google Scholar 

  45. W. Schmid: Boundary value problems for group invariant differential equations. To appear in Proceedings of the Cartan Symposium, Lyon 1984

    Google Scholar 

  46. B. Speh and D. Vogan: Reducibility of generalized principal series representations. Acta Math. 145 (1980), 227–299

    Article  MathSciNet  MATH  Google Scholar 

  47. T. A. Springer: Some results on algebraic groups with involutions. Preprint

    Google Scholar 

  48. D. Vogan: The algebraic structure of the representations of semisimple Lie groups I. Ann. of Math. 109 (1979), 1–60

    Article  MathSciNet  MATH  Google Scholar 

  49. D. Vogan: Representations of Real Reductive Lie Groups. Birkhäuser, Boston 1981

    MATH  Google Scholar 

  50. D. Vogan: Irreducible characters of semisimple Lie groups II. The Kazhdan-Lusztig conjectures. Duke Math. J. 46 (1979), 61–108

    Article  MathSciNet  MATH  Google Scholar 

  51. D. Vogan: Irreducible characters of semisimple Lie groups III. Proof of Kazhdan-Lusztig conjecture in the integral case. Inventiones Math. 71 (1983), 381–417

    Article  MathSciNet  MATH  Google Scholar 

  52. D. Vogan: Understanding the unitary dual. In Lie Group Representations I. Springer Lecture Notes in Mathematics 1024 (1983), pp. 264–288

    Article  MathSciNet  MATH  Google Scholar 

  53. D. Vogan: Unitarizability of certain series of representations. Ann. of Math. 120 (1984), 141–187

    Article  MathSciNet  MATH  Google Scholar 

  54. N. Wallach: Asymptotic expansions of generalized matrix entries of representations of real reductive groups. In Lie Group Representations I. Springer Lecture Notes in Mathematics 1024 (1983), pp. 287–369

    Article  MathSciNet  MATH  Google Scholar 

  55. N. Wallach: On the unitarizability of derived functor modules. Preprint

    Google Scholar 

  56. J. A. Wolf: Unitary Representations on Partially Holomorphic Cohomology Spaces. Amer. Math. Soc. Memoir 138 (1974)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Friedrich Hirzebruch Joachim Schwermer Silke Suter

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Schmid, W. (1985). Recent developments in representation theory. In: Hirzebruch, F., Schwermer, J., Suter, S. (eds) Arbeitstagung Bonn 1984. Lecture Notes in Mathematics, vol 1111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084588

Download citation

  • DOI: https://doi.org/10.1007/BFb0084588

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15195-1

  • Online ISBN: 978-3-540-39298-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics