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Dirac Operators in Representation Theory / by Jing-Song Huang, Pavle Pandzic
(Mathematics: Theory & Applications)
版 | 1st ed. 2006. |
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出版者 | (Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser) |
出版年 | 2006 |
本文言語 | 英語 |
大きさ | XII, 200 p : online resource |
著者標目 | *Huang, Jing-Song author Pandzic, Pavle author SpringerLink (Online service) |
件 名 | LCSH:Topological groups LCSH:Lie groups LCSH:Group theory LCSH:Geometry, Differential LCSH:Operator theory LCSH:Mathematical physics FREE:Topological Groups and Lie Groups FREE:Group Theory and Generalizations FREE:Differential Geometry FREE:Operator Theory FREE:Mathematical Methods in Physics |
一般注記 | 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 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 HTTP:URL=https://doi.org/10.1007/978-0-8176-4493-2 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9780817644932 |
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EB00231122 |
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