| Dirac Operators in Representation Theory 2006 Edition Contributor(s): Huang, Jing-Song (Author), Pandzic, Pavle (Author) |
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ISBN: 0817632182 ISBN-13: 9780817632182 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: July 2006 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Group Theory - Mathematics | Algebra - General |
| Dewey: 515.722 |
| LCCN: 2006923127 |
| Series: Mathematics: Theory & Applications |
| Physical Information: 0.65" H x 6.32" W x 9.36" (1.08 lbs) 200 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This book presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. 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. The book is an excellent contribution to the mathematical literature of representation theory, and 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. |