The Resource Dirac Operators in Representation Theory, by Jing-Song Huang, Pavle Pandzic, (electronic resource)

Dirac Operators in Representation Theory, by Jing-Song Huang, Pavle Pandzic, (electronic resource)

Label
Dirac Operators in Representation Theory
Title
Dirac Operators in Representation Theory
Statement of responsibility
by Jing-Song Huang, Pavle Pandzic
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
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
Member of
http://library.link/vocab/creatorName
Huang, Jing-Song
Dewey number
515.7223
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • 6n3shnRFdC4
  • zyKeG8o3VqU
Language note
English
LC call number
  • QA252.3
  • QA387
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Pandzic, Pavle.
Series statement
Mathematics: Theory & Applications
http://library.link/vocab/subjectName
  • Topological Groups
  • Group theory
  • Global differential geometry
  • Operator theory
  • Mathematical physics
  • Topological Groups, Lie Groups
  • Group Theory and Generalizations
  • Differential Geometry
  • Operator Theory
  • Mathematical Methods in Physics
Label
Dirac Operators in Representation Theory, by Jing-Song Huang, Pavle Pandzic, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [193]-196) and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
1st ed. 2006.
Extent
1 online resource (209 p.)
Form of item
online
Isbn
9786610865901
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-8176-4493-2
Specific material designation
remote
System control number
  • (CKB)1000000000282774
  • (EBL)371686
  • (OCoLC)184984490
  • (SSID)ssj0000139427
  • (PQKBManifestationID)11136607
  • (PQKBTitleCode)TC0000139427
  • (PQKBWorkID)10031821
  • (PQKB)10406069
  • (DE-He213)978-0-8176-4493-2
  • (MiAaPQ)EBC371686
  • (EXLCZ)991000000000282774
Label
Dirac Operators in Representation Theory, by Jing-Song Huang, Pavle Pandzic, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [193]-196) and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
1st ed. 2006.
Extent
1 online resource (209 p.)
Form of item
online
Isbn
9786610865901
Media category
computer
Media type code
  • c
Other control number
10.1007/978-0-8176-4493-2
Specific material designation
remote
System control number
  • (CKB)1000000000282774
  • (EBL)371686
  • (OCoLC)184984490
  • (SSID)ssj0000139427
  • (PQKBManifestationID)11136607
  • (PQKBTitleCode)TC0000139427
  • (PQKBWorkID)10031821
  • (PQKB)10406069
  • (DE-He213)978-0-8176-4493-2
  • (MiAaPQ)EBC371686
  • (EXLCZ)991000000000282774

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