TY  - BOOK
AU  - 
AU  - 
ED  - SpringerLink (Online service)
TI  - Dirac Operators in Representation Theory
T2  - Mathematics: Theory & Applications
SN  - 9780817644932
AV  - QA252.3 
U1  - 512.55 23
PY  - 2006///
CY  - Boston, MA
PB  - Birkhuser 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  - Operator Theory
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; ZDB-2-SMA
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 BottBorelWeil theorem and the AtiyahSchmid 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
UR  - http://dx.doi.org/10.1007/978-0-8176-4493-2
ER  -