Representation Theory, Complex Analysis, and Integral Geometry

This book is an outgrowth of the special term “Harmonic Analysis, Representation Theory, and Integral Geometry,” held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics in Bonn during the summer of 2007.

The contributions in the volume provide a window into a variety of subjects related to reductive groups:  real and complex analysis on homogeneous spaces, arithmetic aspects of moment geometry, geometry of flag varieties, restriction theory of representations, modern aspects of special functions, multiple Dirichlet series, and unfolding identities in the theory of automorphic forms.

Throughout the work, great emphasis was placed on making the articles accessible to interested newcomers to these fields and graduate students. Representation Theory, Complex Analysis, and Integral Geometry aims to stimulate future research in these areas.

Contributors: J. Bernstein, G. Chinta, D. Ciubotaru, J. Faraut, S. Gindikin, J. Jorgenson, J. Kramer, B. Krötz, Y.A. Neretin, K. Nishiyama, O. Offen, H. Schlichtkrull, M.J. Slupinski, R.J. Stanton, B. Speh, P.E. Trapa, T.N.Venkataramana

Preface

1. On Function Spaces on Symmetric Spaces / Bernhard Krötz and Henrik Schlichtkrull

2.  A Relation Involving Rankin-Selberg L-Functions of Cusp Forms and Maass Forms / J. Jorgenson and J. Kramer

3. Orthogonal Period of a Gl3(Z) Eisenstein Series / Gautam Chinta and Omer Offen

4. Regular Orbits of Symmetric Subgroups on Partial Flag Varieties / Dan Ciubotaru, Kyo Nishiyama, and Peter E. Trapa

5. Helgason's Conjecture in Complex Analytical Interior / Simon Gindikin

6. Lectures on Lie Algebras / Joseph Bernstein

7. Stein–Sahi Complementary Series and Their Degenerations / Yuri A. Neretin

8. The Special Symplectic Structure of Binary Cubics / Marcus J. Slupinski and Robert J. Stanton

9. On the Restriction of Representations of Sl(2;C) to Sl(2,R) / B. Speh and T.N.Venkataramana

10. Asymptotics of Spherical Functions for Large Rank: An Introduction / Jacques Faraut