Representation Theory and Automorphic Forms

✍ Scribed by Toshiyuki Kobayashi, Wilfried Schmid, Jae-Hyun Yang

• Publisher: Birkhäuser
• Year: 2008
• Tongue: English
• Leaves: 216
• Series: Progress in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

This volume uses a unified approach to representation theory and automorphic forms. The invited papers, written by leading mathematicians, track recent progress in the ever expanding fields of representation theory and automorphic forms, and their association with number theory and differential geometry.

Representation theory relates to number theory through Langlands’ conjecture, which illuminates the deep properties of primes in number fields. The Langlands program is further analyzed in this work through automorphic functions and automorphic distributions. The relation between representation theory and differential geometry is explored via the Dirac cohomology of Index theory. Also discussed are the subjects of modular forms and harmonic analysis.

The volume also branches off from representation theory into self-dual representations, and includes work from the non-standard geometric view of visible action on complex manifolds towards multiplicity-free representation theory.

Both graduate students and researchers will find inspiration in this volume.

✦ Table of Contents

Preface......Page 8
Contents......Page 6
Irreducibility and Cuspidality......Page 10
On Liftings of Holomorphic Modular Forms......Page 37
Multiplicity-free Theorems of the Restrictions of Unitary Highest Weight Modules with respect to Reductive Symmetric Pairs......Page 53
The Rankin–Selberg Method for Automorphic Distributions......Page 118
Langlands Functoriality Conjecture and Number Theory......Page 158
Discriminant of Certain K3 Surfaces......Page 181