Representation Theory and Automorphic Forms (Progress in Mathematics, 255) - Hardcover

Hardcover

ISBN 10: 0817645055 ISBN 13: 9780817645052

Publisher: Birkhäuser, 2007

Synopsis

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.

About this title

From the Back Cover

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

Edition details

• Publisher: Birkhäuser
• Publication date: 2007
• Language: English
• ISBN 10: 0817645055
• ISBN 13: 9780817645052
• Binding: Hardcover
• Number of pages: 222
• Editor: Toshiyuki Kobayashi, Wilfried Schmid, Jae-Hyun Yang