Arthur's Invariant Trace Formula and Comparison of Inner Forms - Hardcover

Flicker, Yuval Z.

Hardcover

ISBN 10: 3319315919 ISBN 13: 9783319315911

Publisher: Birkhäuser, 2016

Synopsis

This monograph provides an accessible and comprehensive introduction to James Arthur’s invariant trace formula, a crucial tool in the theory of automorphic representations.  It synthesizes two decades of Arthur’s research and writing into one volume, treating a highly detailed and often difficult subject in a clearer and more uniform manner without sacrificing any technical details. 

The book begins with a brief overview of Arthur’s work and a proof of the correspondence between GL(n) and its inner forms in general.  Subsequent chapters develop the invariant trace formula in a form fit for applications, starting with Arthur’s proof of the basic, non-invariant trace formula, followed by a study of the non-invariance of the terms in the basic trace formula, and, finally, an in-depth look at the development of the invariant formula.  The final chapter illustrates the use of the formula by comparing it for G’ = GL(n) and its inner form G< and for functions with matching orbital integrals.

Arthur’s Invariant Trace Formula and Comparison of Inner Forms will appeal to advanced graduate students, researchers, and others interested in automorphic forms and trace formulae.  Additionally, it can be used as a supplemental text in graduate courses on representation theory.

About this title

From the Back Cover

This monograph provides an accessible and comprehensive introduction to James Arthur’s invariant trace formula, a crucial tool in the theory of automorphic representations.  It synthesizes two decades of Arthur’s research and writing into one volume, treating a highly detailed and often difficult subject in a clearer and more uniform manner without sacrificing any technical details.  

The book begins with a brief overview of Arthur’s work and a proof of the correspondence between GL(n) and its inner forms in general.  Subsequent chapters develop the invariant trace formula in a form fit for applications, starting with Arthur’s proof of the basic, non-invariant trace formula, followed by a study of the non-invariance of the terms in the basic trace formula, and, finally, an in-depth look at the development of the invariant formula.  The final chapter illustrates the use of the formula by comparing it for G’ = GL(n) and its inner form G and for functions with matching orbital integrals. 

Arthur’s Invariant Trace Formula and Comparison of Inner Forms will appeal to advanced graduate students, researchers, and others interested in automorphic forms and trace formulae.  Additionally, it can be used as a supplemental text in graduate courses on representation theory.

Edition details

• Publisher: Birkhäuser
• Publication date: 2016
• Language: English
• ISBN 10: 3319315919
• ISBN 13: 9783319315911
• Binding: Hardcover
• Edition number: 1
• Number of pages: 578