000			03844nam a22005895i 4500
001			978-0-8176-4493-2
003			DE-He213
005			20161121231029.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780817644932 _9978-0-8176-4493-2
024	7		_a10.1007/978-0-8176-4493-2 _2doi
050		4	_aQA252.3
050		4	_aQA387
072		7	_aPBG _2bicssc
072		7	_aMAT014000 _2bisacsh
072		7	_aMAT038000 _2bisacsh
082	0	4	_a512.55 _223
082	0	4	_a512.482 _223
100	1		_aHuang, Jing-Song. _eauthor.
245	1	0	_aDirac Operators in Representation Theory _h[electronic resource] / _cby Jing-Song Huang, Pavle Pandžić.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2006.
300			_aXII, 200 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aMathematics: Theory & Applications
505	0		_aLie 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.
520			_aThis 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.
650		0	_aMathematics.
650		0	_aGroup theory.
650		0	_aTopological groups.
650		0	_aLie groups.
650		0	_aOperator theory.
650		0	_aDifferential geometry.
650		0	_aPhysics.
650	1	4	_aMathematics.
650	2	4	_aTopological Groups, Lie Groups.
650	2	4	_aGroup Theory and Generalizations.
650	2	4	_aDifferential Geometry.
650	2	4	_aOperator Theory.
650	2	4	_aMathematical Methods in Physics.
700	1		_aPandžić, Pavle. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817632182
830		0	_aMathematics: Theory & Applications
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4493-2
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c507532 _d507532