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# Dirac Operators in Representation Theory

US$169.00 (If any tax is payable it will be calculated and shown at checkout.) This monograph presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Dirac operators are widely used in physics, differential geometry, and group-theoretic settings (particularly, the geometric construction of discrete series representations). The related concept of Dirac cohomology, which is defined using Dirac operators, is a far-reaching generalization that connects index theory in differential geometry to representation theory. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective. Key topics covered include: * Proof of Vogan's conjecture on Dirac cohomology * Simple proofs of many classical theorems, such as the Bott–Borel–Weil theorem and the Atiyah–Schmid theorem * Dirac cohomology, defined by Kostant's cubic Dirac operator, along with other closely related kinds of cohomology, such as n-cohomology and (g,K)-cohomology * Cohomological parabolic induction and$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.

Birkhäuser Boston; May 2007
209 pages; ISBN 9780817644932
Title: Dirac Operators in Representation Theory
Author: Jing-Song Huang; Pavle Pandzic

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ISBNs
0817644938
9780817632182
9780817644932