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|a 9780817644932
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|a Huang, Jing-Song
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| 245 |
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|a Dirac Operators in Representation Theory
|h Elektronische Ressource
|c by Jing-Song Huang, Pavle Pandzic
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| 250 |
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|a 1st ed. 2006
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| 260 |
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|a Boston, MA
|b Birkhäuser
|c 2006, 2006
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| 300 |
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|a XII, 200 p
|b online resource
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| 505 |
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|a 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
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| 653 |
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|a Group Theory and Generalizations
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| 653 |
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|a Geometry, Differential
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| 653 |
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|a Group theory
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| 653 |
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|a Topological Groups and Lie Groups
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| 653 |
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|a Lie groups
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| 653 |
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|a Topological groups
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| 653 |
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|a Operator theory
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| 653 |
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|a Mathematical physics
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| 653 |
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|a Operator Theory
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| 653 |
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|a Differential Geometry
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| 653 |
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|a Mathematical Methods in Physics
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| 700 |
1 |
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|a Pandzic, Pavle
|e [author]
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
0 |
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|a Mathematics: Theory & Applications
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| 028 |
5 |
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|a 10.1007/978-0-8176-4493-2
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| 856 |
4 |
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|u https://doi.org/10.1007/978-0-8176-4493-2?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 512.482
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| 082 |
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|a 512.55
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| 520 |
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|a 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
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