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- Unitarian_trick abstract "In mathematics, the unitarian trick is a device in the representation theory of Lie groups, introduced by Adolf Hurwitz (1897) for the special linear group and by Hermann Weyl for general semisimple groups. It applies to show that the representation theory of some group G is in a qualitative way controlled by that of some other compact group K. An important example is that in which G is the complex general linear group, and K the unitary group acting on vectors of the same size. From the fact that the representations of K are completely reducible, the same is concluded for those of G, at least in finite dimensions.The relationship between G and K that drives this connection is traditionally expressed in the terms that the Lie algebra of K is a real form of that of G. In the theory of algebraic groups, the relationship can also be put that K is a dense subset of G, for the Zariski topology.The trick works for reductive Lie groups, of which an important case are semisimple Lie groups.".
- Unitarian_trick wikiPageID "1569065".
- Unitarian_trick wikiPageLength "2855".
- Unitarian_trick wikiPageOutDegree "25".
- Unitarian_trick wikiPageRevisionID "670675537".
- Unitarian_trick wikiPageWikiLink Adolf_Hurwitz.
- Unitarian_trick wikiPageWikiLink Algebraic_group.
- Unitarian_trick wikiPageWikiLink Category:Representation_theory_of_Lie_groups.
- Unitarian_trick wikiPageWikiLink Compact_group.
- Unitarian_trick wikiPageWikiLink Covering_space.
- Unitarian_trick wikiPageWikiLink Dense_set.
- Unitarian_trick wikiPageWikiLink General_linear_group.
- Unitarian_trick wikiPageWikiLink Hermann_Weyl.
- Unitarian_trick wikiPageWikiLink Issai_Schur.
- Unitarian_trick wikiPageWikiLink Lie_algebra.
- Unitarian_trick wikiPageWikiLink Lie_group.
- Unitarian_trick wikiPageWikiLink Mathematics.
- Unitarian_trick wikiPageWikiLink Orthogonal_group.
- Unitarian_trick wikiPageWikiLink Real_form_(Lie_theory).
- Unitarian_trick wikiPageWikiLink Reductive_group.
- Unitarian_trick wikiPageWikiLink Representation_theory.
- Unitarian_trick wikiPageWikiLink Semi-simplicity.
- Unitarian_trick wikiPageWikiLink Semisimple_Lie_algebra.
- Unitarian_trick wikiPageWikiLink Unitary_group.
- Unitarian_trick wikiPageWikiLink Zariski_topology.
- Unitarian_trick wikiPageWikiLinkText "Unitarian trick".
- Unitarian_trick wikiPageWikiLinkText "unitarian trick".
- Unitarian_trick authorlink "Adolf Hurwitz".
- Unitarian_trick first "Adolf".
- Unitarian_trick last "Hurwitz".
- Unitarian_trick wikiPageUsesTemplate Template:Citation.
- Unitarian_trick wikiPageUsesTemplate Template:Harvs.
- Unitarian_trick wikiPageUsesTemplate Template:Main.
- Unitarian_trick wikiPageUsesTemplate Template:Reflist.
- Unitarian_trick year "1897".
- Unitarian_trick subject Category:Representation_theory_of_Lie_groups.
- Unitarian_trick hypernym Device.
- Unitarian_trick type Device.
- Unitarian_trick comment "In mathematics, the unitarian trick is a device in the representation theory of Lie groups, introduced by Adolf Hurwitz (1897) for the special linear group and by Hermann Weyl for general semisimple groups. It applies to show that the representation theory of some group G is in a qualitative way controlled by that of some other compact group K. An important example is that in which G is the complex general linear group, and K the unitary group acting on vectors of the same size.".
- Unitarian_trick label "Unitarian trick".
- Unitarian_trick sameAs Q7887223.
- Unitarian_trick sameAs m.05c47g.
- Unitarian_trick sameAs Q7887223.
- Unitarian_trick wasDerivedFrom Unitarian_trick?oldid=670675537.
- Unitarian_trick isPrimaryTopicOf Unitarian_trick.