This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the 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. In addition, the volume branches off from representation theory into self-dual representations, and includes work from the non-standard geometric view of viable action on complex manifolds towards multiplicity-free representation theory.

Interdisciplinary approach to the ever expanding fields of representation theory and automorphic forms Written by leading mathematicians Tracks recent progress in representation theory and automorphic forms, and their association with number theory and differential geometry Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture

Klappentext

This volume addresses the interplay between 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 the Langlands program, which conjecturally connects algebraic extensions of number fields to automorphic representations and L-functions. These are the subject of several of the papers. Multiplicity-free representations constitute another subject, which is approached geometrically via the notion of visible group actions on complex manifolds.

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

Contributors: T. Ikeda, T. Kobayashi, S. Miller, D. Ramakrishnan, W. Schmid, F. Shahidi, K. Yoshikawa

Inhalt
Irreducibility and Cuspidality.- On Liftings of Holomorphic Modular Forms.- Multiplicity-free Theorems of the Restrictions of Unitary Highest Weight Modules with respect to Reductive Symmetric Pairs.- The RankinSelberg Method for Automorphic Distributions.- Langlands Functoriality Conjecture and Number Theory.- Discriminant of Certain K3 Surfaces.