Dirac Operators in Representation Theory

• Main Authors: Huang, Jing-Song (Author), Pandžić, Pavle (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2006.
• Series: Mathematics: Theory & Applications
• Subjects: Mathematics.; Group theory.; Topological groups.; Lie groups.; Operator theory.; Differential geometry.; Physics.; Topological Groups, Lie Groups.; Group Theory and Generalizations.; Differential Geometry.; Operator Theory.; Mathematical Methods in Physics.

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...

Table of Contents:

• 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.