Advertisement

Geometric Methods in Representation Theory

  • Gregg J. Zuckerman
Part of the Progress in Mathematics book series (PM, volume 40)

Abstract

This lecture is a brief introduction to the relationship between the algebraic geometry of flag varieties and the representation theory of reductive Lie algebras and real reductive Lie groups. The author would like to thank the organizers of this conference for the opportunity to make a presentation.

Keywords

Irreducible Character Discrete Series Borel Subgroup Local Cohomology Flag Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. Adams, “Some results on the dual pair (O(p,q), Sp(2m)).” Yale University thesis (1981).Google Scholar
  2. [2]
    A. Beilinson, J. Bernstein. Localisation de ℊ-modules. C.R. Acad. Sc. Paris, T. 292 (1981), 15–18.Google Scholar
  3. [3]
    J.L. Brylinski, M. Kashiwara. Kazhdan — Lusztig conjecture and holonomic systems. Inv. Math. 64, 387–410 (1981).CrossRefGoogle Scholar
  4. [4]
    T. Enright. On the fundamental series of a real semisimple Lie algebra: their irreducibility, resolutions, and multiplicity formulae. Ann. of Math. 110 (1979), 1–82.CrossRefGoogle Scholar
  5. [5]
    R. Hartshorne. “Local Cohomology.” (Based on lectures of A. Grothendieck.) Lecture Notes in Math., Springer-Verlag, Berlin (1967).Google Scholar
  6. [6]
    G. Kempf. The Grothendieck-Cousin complex of an induced representation. Adv. in Math. 29, 310–396 (1978).CrossRefGoogle Scholar
  7. [7]
    W. Schmid. “Homogeneous complex manifolds and representations of semisimple Lie groups.” Univ. of Calif. at Berkeley thesis, (1967).Google Scholar
  8. [8]
    D. Vogan. “Representations of real reductive Lie groups.” Birkhauser, Boston (1981).Google Scholar
  9. [9]
    D. Vogan. Irreducible characters of semisimple Lie groups III. Proof of the Kazhdan-Lusztig conjecture in the integral case. To appear in Inv. Math (1981).Google Scholar
  10. [10]
    G.J. Zuckerman. Some character identities for semisimple Lie groups. Princeton University thesis, (1974).Google Scholar
  11. [11]
    G.J. Zuckerman. Coherent translation of characters of semisimple Lie groups. “Proceedings of the International Congress of Mathematicians,” Helsinki (1978).Google Scholar

Copyright information

© Birkhäuser Boston, Inc. 1983

Authors and Affiliations

  • Gregg J. Zuckerman

There are no affiliations available

Personalised recommendations