Geometry and Representation Theory of Real and p-adic groups

1. Front Matter

   Pages i-x

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2. The Spherical Dual for p-adic Groups

   • Dan Barbasch

   Pages 1-19

3. Finite Rank Homogeneous Holomorphic Bundles in Flag Spaces

   • Tim Bratten

   Pages 21-34

4. Etale Affine Representations of Lie Groups

   • Dietrich Burde

   Pages 35-44

5. Compatibility Between a Geometric Character Formula and the Induced Character Formula

   • Esther Galina

   Pages 45-56

6. An Action of the R-group on the Langlands Subrepresentations

   • Eugenio Garnica Vigil

   Pages 57-67

7. Geometric Quantization for Nilpotent Coadjoint Orbits

   • William Graham, David A. Vogan Jr.

   Pages 69-137

8. A Remark on Casselman’s Comparison Theorem

   • Henryk Hecht, Joseph L. Taylor

   Pages 139-146

9. Principal Covariants, Multiplicity-Free Actions, and the K-types of Holomorphic Discrete Series

   • Roger Howe, Hanspeter Kraft

   Pages 147-161

10. Whittaker Models for Carayol Representations of GL _N (F)

    • Roberto Johnson

    Pages 163-174

11. Smooth Representations of Reductive p-adic Groups

    • Philip C. Kutzko

    Pages 175-196

12. Regular Metabelian Lie Algebras

    • Fernando Levstein, Alejandro Tiraboschi

    Pages 197-207

13. Equivariant Derived Categories, Zuckerman Functors and Localization

    • Dragan Miličić, Pavle Pandžić

    Pages 209-242

14. A Comparison of Geometric Theta Functions for Forms of Orthogonal Groups

    • Jürgen Rohlfs, Birgit Speh

    Pages 243-272

15. Flag Manifolds and Representation Theory

    • Joseph A. Wolf

    Pages 273-323

16. Back Matter

    Pages 325-326

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The representation theory of Lie groups plays a central role in both clas­ sical and recent developments in many parts of mathematics and physics. In August, 1995, the Fifth Workshop on Representation Theory of Lie Groups and its Applications took place at the Universidad Nacional de Cordoba in Argentina. Organized by Joseph Wolf, Nolan Wallach, Roberto Miatello, Juan Tirao, and Jorge Vargas, the workshop offered expository courses on current research, and individual lectures on more specialized topics. The present vol­ ume reflects the dual character of the workshop. Many of the articles will be accessible to graduate students and others entering the field. Here is a rough outline of the mathematical content. (The editors beg the indulgence of the readers for any lapses in this preface in the high standards of historical and mathematical accuracy that were imposed on the authors of the articles. ) Connections between flag varieties and representation theory for real re­ ductive groups have been studied for almost fifty years, from the work of Gelfand and Naimark on principal series representations to that of Beilinson and Bernstein on localization. The article of Wolf provides a detailed introduc­ tion to the analytic side of these developments. He describes the construction of standard tempered representations in terms of square-integrable partially harmonic forms (on certain real group orbits on a flag variety), and outlines the ingredients in the Plancherel formula. Finally, he describes recent work on the complex geometry of real group orbits on partial flag varieties.

• Geometry
• Grad
• Mathematics
• algebra
• representation theory

• Facultad de Mathemática, Astronomia y Fisica, Universidad Nacional de Córdoba Ciudad Universitaria, Córdoba, Argentina

  Juan Tirao

• Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

  David A. Vogan

• Department of Mathematics, University of California, Berkeley, USA

  Joseph A. Wolf

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