About: Borel–Weil–Bott theorem

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In mathematics, the Borel–Weil–Bott theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can be obtained from holomorphic sections of certain complex vector bundles, and, more generally, from higher sheaf cohomology groups associated to such bundles. It is built on the earlier Borel–Weil theorem of Armand Borel and André Weil, dealing just with the space of sections (the zeroth cohomology group), the extension to higher cohomology groups being provided by Raoul Bott. One can equivalently, through Serre's GAGA, view this as a result in complex algebraic geometry in the Zariski topology.

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rdf:type	yago:WikicatTheoremsInRepresentationTheory yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Borel–Weil–Bott theorem (en) 보렐-베유-보트 정리 (ko)
rdfs:comment	In mathematics, the Borel–Weil–Bott theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can be obtained from holomorphic sections of certain complex vector bundles, and, more generally, from higher sheaf cohomology groups associated to such bundles. It is built on the earlier Borel–Weil theorem of Armand Borel and André Weil, dealing just with the space of sections (the zeroth cohomology group), the extension to higher cohomology groups being provided by Raoul Bott. One can equivalently, through Serre's GAGA, view this as a result in complex algebraic geometry in the Zariski topology. (en) 리 군 이론에서, 보렐-베유-보트 정리(영어: Borel–Weil–Bott theorem)는 반단순 리 군의 기약 표현을 어떤 복소수 선다발의 층 코호몰로지 군으로 나타내는 정리이다. (ko)
dct:subject	Representation theory of Lie groups Theorems in representation theory
Wikipage page ID	725331 (xsd:integer)
Wikipage revision ID	1106153381 (xsd:integer)
Link from a Wikipage to another Wikipage	Representation theory Algebraically closed field Homogeneous space Inventiones Mathematicae Lie group Representation theory of Lie groups Compact Lie group Complex numbers Mathematics Quotient group GAGA Connected space André Weil Complex manifold Irreducible representation Line bundle Linear algebraic group Semisimple algebraic group Kempf vanishing theorem Jacob Lurie Riemann sphere Armand Borel Symmetric power Homogeneous coordinates Homogeneous polynomial Maximal torus Weight (representation theory) Borel subgroup Theorems in representation theory Integer Canonical bundle Cartan subgroup Raoul Bott Semisimple Lie group Flag manifold Special linear group Section (fiber bundle) Sheaf (mathematics) Vector bundle Complex algebraic geometry Principal bundle Zariski topology Sheaf cohomology Real form (Lie theory) Theorem of the highest weight SL2(C) Weyl group Associated fiber bundle Flag variety Highest weight representation Complex projective line Unipotent radical Holomorphic line bundle Holomorphic map Irreducible unitary representation
Link from a Wikipage to an external page	http://store.doverpublications.com/0486797295.html http://www.math.harvard.edu/~lurie/papers/bwb.pdf
sameAs	Borel–Weil–Bott theorem Borel–Weil–Bott theorem Borel–Weil–Bott theorem Borel–Weil–Bott theorem
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id	4585 (xsd:integer) b/b120400 (en)
title	Borel–Bott–Weil theorem (en) Bott–Borel–Weil theorem (en)
has abstract	In mathematics, the Borel–Weil–Bott theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can be obtained from holomorphic sections of certain complex vector bundles, and, more generally, from higher sheaf cohomology groups associated to such bundles. It is built on the earlier Borel–Weil theorem of Armand Borel and André Weil, dealing just with the space of sections (the zeroth cohomology group), the extension to higher cohomology groups being provided by Raoul Bott. One can equivalently, through Serre's GAGA, view this as a result in complex algebraic geometry in the Zariski topology. (en) 리 군 이론에서, 보렐-베유-보트 정리(영어: Borel–Weil–Bott theorem)는 반단순 리 군의 기약 표현을 어떤 복소수 선다발의 층 코호몰로지 군으로 나타내는 정리이다. (ko)
gold:hypernym	Result
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foaf:isPrimaryTopicOf	wikipedia-en:Borel–Weil–Bott_theorem
is Link from a Wikipage to another Wikipage of	BBW List of eponyms (A–K)

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