Huang, Jing-Song. <br/><br/>
Dirac Operators in Representation Theory  [electronic resource] / 
by Jing-Song Huang, Pavle Pandžić. 
 - X, 199p.  online resource. 
 - Mathematics: Theory & Applications .
 - Mathematics: Theory & Applications .
<br/><br/>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. 
<br/><br/> 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. 
<br/><br/><label>ISBN: </label>9780817644932 99780817644932 
<br/><br/><label>Standard No.: </label>10.1007/978-0-8176-4493-2  doi 
<br/><br/><label>Subjects--Topical Terms: </label><br/>MATHEMATICS.<br/>GROUP THEORY.<br/>TOPOLOGICAL GROUPS.<br/>OPERATOR THEORY.<br/>GLOBAL DIFFERENTIAL GEOMETRY.<br/>MATHEMATICAL PHYSICS.<br/>MATHEMATICS.<br/>TOPOLOGICAL GROUPS, LIE GROUPS.<br/>GROUP THEORY AND GENERALIZATIONS.<br/>DIFFERENTIAL GEOMETRY.<br/>OPERATOR THEORY.<br/>MATHEMATICAL METHODS IN PHYSICS.
<br/><br/><label>Dewey Class. No.: </label>512.55 512.482