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The Resource Dirac Operators in Representation Theory, by JingSong Huang, Pavle Pandzic, (electronic resource)
Dirac Operators in Representation Theory, by JingSong Huang, Pavle Pandzic, (electronic resource)
Resource Information
The item Dirac Operators in Representation Theory, by JingSong Huang, Pavle Pandzic, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Dirac Operators in Representation Theory, by JingSong Huang, Pavle Pandzic, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 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 grouptheoretic settings (particularly, the geometric construction of discrete series representations). The related concept of Dirac cohomology, which is defined using Dirac operators, is a farreaching 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 ncohomology 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 selfcontained 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
 Language

 eng
 eng
 Edition
 1st ed. 2006.
 Extent
 1 online resource (209 p.)
 Note
 Description based upon print version of record
 Contents

 Lie Groups, Lie Algebras and Representations
 Clifford Algebras and Spinors
 Dirac Operators in the Algebraic Setting
 A Generalized BottBorelWeil 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
 Isbn
 9786610865901
 Label
 Dirac Operators in Representation Theory
 Title
 Dirac Operators in Representation Theory
 Statement of responsibility
 by JingSong Huang, Pavle Pandzic
 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 grouptheoretic settings (particularly, the geometric construction of discrete series representations). The related concept of Dirac cohomology, which is defined using Dirac operators, is a farreaching 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 ncohomology 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 selfcontained 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://library.link/vocab/creatorName
 Huang, JingSong
 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 JingSong Huang, Pavle Pandzic, (electronic resource)
 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 BottBorelWeil 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
 10.1007/9780817644932
 Specific material designation
 remote
 System control number

 (CKB)1000000000282774
 (EBL)371686
 (OCoLC)184984490
 (SSID)ssj0000139427
 (PQKBManifestationID)11136607
 (PQKBTitleCode)TC0000139427
 (PQKBWorkID)10031821
 (PQKB)10406069
 (DEHe213)9780817644932
 (MiAaPQ)EBC371686
 (EXLCZ)991000000000282774
 Label
 Dirac Operators in Representation Theory, by JingSong Huang, Pavle Pandzic, (electronic resource)
 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 BottBorelWeil 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
 10.1007/9780817644932
 Specific material designation
 remote
 System control number

 (CKB)1000000000282774
 (EBL)371686
 (OCoLC)184984490
 (SSID)ssj0000139427
 (PQKBManifestationID)11136607
 (PQKBTitleCode)TC0000139427
 (PQKBWorkID)10031821
 (PQKB)10406069
 (DEHe213)9780817644932
 (MiAaPQ)EBC371686
 (EXLCZ)991000000000282774
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.umanitoba.ca/portal/DiracOperatorsinRepresentationTheoryby/myYGD3RnC34/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.umanitoba.ca/portal/DiracOperatorsinRepresentationTheoryby/myYGD3RnC34/">Dirac Operators in Representation Theory, by JingSong Huang, Pavle Pandzic, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.lib.umanitoba.ca/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.umanitoba.ca/">University of Manitoba Libraries</a></span></span></span></span></div>