Developments and Retrospectives in Lie Theory

1. Front Matter

   Pages i-ix

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2. Group Gradings on Lie Algebras and Applications to Geometry: II

   • Yuri Bahturin, Michel Goze, Elisabeth Remm

   Pages 1-40

3. Harmonic Analysis on Homogeneous Complex Bounded Domains and Noncommutative Geometry

   • Pierre Bieliavsky, Victor Gayral, Axel de Goursac, Florian Spinnler

   Pages 41-76

4. The Radon Transform and Its Dual for Limits of Symmetric Spaces

   • Joachim Hilgert, Gestur Ólafsson

   Pages 77-111

5. Cycle Connectivity and Automorphism Groups of Flag Domains

   • Alan Huckleberry

   Pages 113-126

6. Shintani Functions, Real Spherical Manifolds, and Symmetry Breaking Operators

   • Toshiyuki Kobayashi

   Pages 127-159

7. Harmonic Spinors on Reductive Homogeneous Spaces

   • Salah Mehdi, Roger Zierau

   Pages 161-181

8. Twisted Harish–Chandra Sheaves and Whittaker Modules: The Nondegenerate Case

   • Dragan Miličić, Wolfgang Soergel

   Pages 183-196

9. Unitary Representations of Unitary Groups

   • Karl-Hermann Neeb

   Pages 197-243

10. Weak Splittings of Quotients of Drinfeld and Heisenberg Doubles

    • Milen Yakimov

    Pages 245-268

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. At the beginning, the top universities in California and Utah hosted the meetings, which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. These Lie theory workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. The contributors have all participated in these Lie theory workshops and include in this volume expository articles which will cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.

• Artinian Gorenstein algebras
• Dirac Cohmology
• harmonic analysis
• mathematical physics
• representation theory
• unitary representations of Banach

• Department of Mathematics, University of California, Santa Cruz, Santa Cruz, USA

  Geoffrey Mason

• School of Engineering and Science, Jacobs University, Bremen, Germany

  Ivan Penkov

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

  Joseph A. Wolf

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