| Description |
1 online resource (x, 199 pages) |
| Series |
Mathematics, theory & applications |
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Mathematics (Boston, Mass.)
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| 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 |
| Summary |
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 |
|
"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."--Publisher's website |
| Bibliography |
Includes bibliographical references (pages 193-196) and index |
| Notes |
English |
|
Print version record |
| In |
OhioLINK electronic book center |
|
SpringerLink |
| Subject |
Representations of groups.
|
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Dirac equation.
|
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Differential operators.
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MATHEMATICS -- Functional Analysis.
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Differential operators.
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Representations of groups.
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Dirac equation.
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Representaciones de grupos
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Differential operators
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Dirac equation
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Representations of groups
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| Form |
Electronic book
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| Author |
Pandžić, Pavle, author
|
| ISBN |
0817644938 |
|
9780817644932 |
|
