Mathematics: Theory & Applications

Dirac Operators in Representation Theory

Authors: Huang, Jing-Song, Pandzic, Pavle

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eBook 101,14 €
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  • ISBN 978-0-8176-4493-2
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Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-0-8176-3218-2
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About this book

This monograph presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Dirac operators are widely used in physics, differential geometry, and group-theoretic settings (particularly, the geometric construction of discrete series representations). The related concept of Dirac cohomology, which is defined using Dirac operators, is a far-reaching generalization that connects index theory in differential geometry to representation theory. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective.

Key topics covered include:

* Proof of Vogan's conjecture on Dirac cohomology

* Simple proofs of many classical theorems, such as the Bott–Borel–Weil theorem and the Atiyah–Schmid theorem

* Dirac cohomology, defined by Kostant's cubic Dirac operator, along with other closely related kinds of cohomology, such as n-cohomology and (g,K)-cohomology

* Cohomological parabolic induction and $A_q(\lambda)$ modules

* Discrete series theory, characters, existence and exhaustion

* Sharpening of the Langlands formula on multiplicity of automorphic forms, with applications

* Dirac cohomology for Lie superalgebras

An excellent contribution to the mathematical literature of representation theory, this self-contained exposition offers a systematic examination and panoramic view of the subject. The material will be of interest to researchers and graduate students in representation theory, differential geometry, and physics.

Reviews

This book contains a more detailed explanation of the results from several recent papers of the authors. The book is aimed at a somewhat broader audience. Clifford algebras are presented rather thoroughly. Some basics of Lie groups and their representations are mostly relegated to earlier literature. There is a good introduction to the so-called cohomological induction, which is short but still gives the main ideas of some parts of the proofs. – MathSciNet


Buy this book

eBook 101,14 €
price for Spain (gross)
  • ISBN 978-0-8176-4493-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-0-8176-3218-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Dirac Operators in Representation Theory
Authors
Series Title
Mathematics: Theory & Applications
Copyright
2006
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4493-2
DOI
10.1007/978-0-8176-4493-2
Hardcover ISBN
978-0-8176-3218-2
Edition Number
1
Number of Pages
XII, 200
Topics