Dirac Operators in Representation Theory [electronic resource] /
by Jing-Song Huang, Pavle Pandʾi.
- XII, 200 p. online resource.
- Mathematics: Theory & Applications .
- Mathematics: Theory & Applications .
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
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
9780817644932
10.1007/978-0-8176-4493-2 doi
Mathematics. Group theory. Topological Groups. Operator theory. Global differential geometry. Mathematical physics. Mathematics. Topological Groups, Lie Groups. Group Theory and Generalizations. Differential Geometry. Operator Theory. Mathematical Methods in Physics.