Representation theory, complex analysis, and integral geometry

✍ Scribed by Bernhard Krötz, Henrik Schlichtkrull (auth.), Bernhard Krötz, Omer Offen, Eitan Sayag (eds.)

• Publisher: Birkhäuser Basel
• Year: 2012
• Tongue: English
• Leaves: 286
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-x
On Function Spaces on Symmetric Spaces....Pages 1-8
A Relation Involving Rankin–Selberg L -Functions of Cusp Forms and Maass Forms....Pages 9-40
Orthogonal Period of a GL 3 ( ℤ ) Eisenstein Series....Pages 41-59
Regular Orbits of Symmetric Subgroups on Partial Flag Varieties....Pages 61-86
Helgason’s Conjecture in Complex Analytical Interior....Pages 87-95
Lectures on Lie Algebras....Pages 97-132
Stein–Sahi Complementary Series and Their Degenerations....Pages 133-183
The Special Symplectic Structure of Binary Cubics....Pages 185-230
On the Restriction of Representations of SL(2, ℂ) to SL(2, ℝ)....Pages 231-249
Asympotics of Spherical Functions For Large Rank: An Introduction....Pages 251-275

✦ Subjects

Group Theory and Generalizations; Topological Groups, Lie Groups; Analysis; Differential Geometry; Algebra; Number Theory