Representation theory and automorphic forms

Toshiyuki Kobayashi, Wilfried Schmid, Jae-Hyun Yang0817645055, 9780817645052, 9780817646462

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.

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Table of contents :
Preface……Page 7
Contents……Page 5
Irreducibility and Cuspidality……Page 9
On Liftings of Holomorphic Modular Forms……Page 36
Multiplicity-free Theorems of the Restrictions of Unitary Highest Weight Modules with respect to Reductive Symmetric Pairs……Page 52
The Rankin–Selberg Method for Automorphic Distributions……Page 117
Langlands Functoriality Conjecture and Number Theory……Page 157
Discriminant of Certain K3 Surfaces……Page 180