TY  - BOOK
AU  - Huang,Jing-Song
AU  - Pandžić,Pavle
ED  - SpringerLink (Online service)
TI  - Dirac Operators in Representation Theory
T2  - Mathematics: Theory & Applications
SN  - 9780817644932
U1  - 512.55 23
PY  - 2006///
CY  - Boston, MA
PB  - Birkhäuser Boston
KW  - MATHEMATICS
KW  - GROUP THEORY
KW  - TOPOLOGICAL GROUPS
KW  - OPERATOR THEORY
KW  - GLOBAL DIFFERENTIAL GEOMETRY
KW  - MATHEMATICAL PHYSICS
KW  - TOPOLOGICAL GROUPS, LIE GROUPS
KW  - GROUP THEORY AND GENERALIZATIONS
KW  - DIFFERENTIAL GEOMETRY
KW  - MATHEMATICAL METHODS IN PHYSICS
N1  - Lie Groups, Lie Algebras and Representations -- Clifford Algebras and Spinors -- Dirac Operators in the Algebraic Setting -- A Generalized Bott-Borel-Weil Theorem -- Cohomological Induction -- Properties of Cohomologically Induced Modules -- Discrete Series -- Dimensions of Spaces of Automorphic Forms -- Dirac Operators and Nilpotent Lie Algebra Cohomology -- Dirac Cohomology for Lie Superalgebras
N2  - 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
UR  - http://dx.doi.org/10.1007/978-0-8176-4493-2
ER  -