Borel–Weil–Bott theorem
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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Armand BorelBBWBBW theoremBWB theoremBorel-Bott-Weil theoremBorel-Weil-Bott constructionBorel-Weil-Bott theoremBorel-Weil theoremBorel-Weyl theoremBorel–Bott–Weil theoremBorel–Weil theoremBottBott-Borel-Weil theoremBott–Borel–Weil theoremCoadjoint representationComplexification (Lie group)Deligne–Lusztig theoryDiscrete series representationEquivariant sheafGlossary of Lie groups and Lie algebrasGlossary of representation theoryJordan mapKempf vanishing theoremLinear algebraic groupList of Lie groups topicsList of eponyms (A–K)List of representation theory topicsList of theoremsList of things named after André WeilRaoul BottReductive groupRepresentation theory of SU(2)Representation theory of semisimple Lie algebrasRepresentation theory of the Lorentz groupSheaf (mathematics)Séminaire Nicolas Bourbaki (1950–1959)Theorem of the highest weightTopological quantum field theoryWeyl module
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Borel–Weil–Bott theorem
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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In mathematics, the Borel–Weil ...... metry in the Zariski topology.
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Borel–Bott–Weil theorem
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Bott–Borel–Weil theorem
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In mathematics, the Borel–Weil ...... metry in the Zariski topology.
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Borel–Weil–Bott theorem
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