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- Langlands_dual_group abstract "In representation theory, a branch of mathematics, the Langlands dual LG of a reductive algebraic group G (also called the L-group of G) is a group that controls the representation theory of G. If G is defined over a field k, then LG is an extension of the absolute Galois group of k by a complex Lie group. There is also a variation called the Weil form of the L-group, where the Galois group is replaced by a Weil group. The Langlands dual group is also often referred to as an L-group; here the letter L indicates also the connection with the theory of L-functions, particularly the automorphic L-functions. The Langlands dual was introduced by Langlands (1967) in a letter to A. Weil. The L-group is used heavily in the Langlands conjectures of Robert Langlands. It is used to make precise statements from ideas that automorphic forms are in a sense functorial in the group G, when k is a global field. It is not exactly G with respect to which automorphic forms and representations are functorial, but LG. This makes sense of numerous phenomena, such as 'lifting' of forms from one group to another larger one, and the general fact that certain groups that become isomorphic after field extensions have related automorphic representations.".
- Langlands_dual_group wikiPageExternalLink pspum332.
- Langlands_dual_group wikiPageExternalLink weil1967.
- Langlands_dual_group wikiPageExternalLink pspum332-ptIII-2.pdf.
- Langlands_dual_group wikiPageID "6789133".
- Langlands_dual_group wikiPageLength "6909".
- Langlands_dual_group wikiPageOutDegree "26".
- Langlands_dual_group wikiPageRevisionID "638730958".
- Langlands_dual_group wikiPageWikiLink A._Borel.
- Langlands_dual_group wikiPageWikiLink A._Weil.
- Langlands_dual_group wikiPageWikiLink Absolute_Galois_group.
- Langlands_dual_group wikiPageWikiLink Affine_Grassmannian.
- Langlands_dual_group wikiPageWikiLink André_Weil.
- Langlands_dual_group wikiPageWikiLink Annals_of_Mathematics.
- Langlands_dual_group wikiPageWikiLink Armand_Borel.
- Langlands_dual_group wikiPageWikiLink Automorphic_form.
- Langlands_dual_group wikiPageWikiLink Category:Automorphic_forms.
- Langlands_dual_group wikiPageWikiLink Category:Class_field_theory.
- Langlands_dual_group wikiPageWikiLink Category:Representation_theory_of_Lie_groups.
- Langlands_dual_group wikiPageWikiLink Category_(mathematics).
- Langlands_dual_group wikiPageWikiLink Complex_Lie_group.
- Langlands_dual_group wikiPageWikiLink Dynkin_diagram.
- Langlands_dual_group wikiPageWikiLink Field_(mathematics).
- Langlands_dual_group wikiPageWikiLink Field_extension.
- Langlands_dual_group wikiPageWikiLink Functor.
- Langlands_dual_group wikiPageWikiLink Functorial.
- Langlands_dual_group wikiPageWikiLink Global_field.
- Langlands_dual_group wikiPageWikiLink L-function.
- Langlands_dual_group wikiPageWikiLink Langlands_conjectures.
- Langlands_dual_group wikiPageWikiLink Langlands_group.
- Langlands_dual_group wikiPageWikiLink Langlands_program.
- Langlands_dual_group wikiPageWikiLink Reductive_algebraic_group.
- Langlands_dual_group wikiPageWikiLink Reductive_group.
- Langlands_dual_group wikiPageWikiLink Representation_theory.
- Langlands_dual_group wikiPageWikiLink Robert_Langlands.
- Langlands_dual_group wikiPageWikiLink Root_datum.
- Langlands_dual_group wikiPageWikiLink Weil_group.
- Langlands_dual_group wikiPageWikiLinkText "L-group".
- Langlands_dual_group wikiPageWikiLinkText "Langlands dual group".
- Langlands_dual_group hasPhotoCollection Langlands_dual_group.
- Langlands_dual_group wikiPageUsesTemplate Template:Citation.
- Langlands_dual_group wikiPageUsesTemplate Template:Distinguish.
- Langlands_dual_group wikiPageUsesTemplate Template:Harvtxt.
- Langlands_dual_group subject Category:Automorphic_forms.
- Langlands_dual_group subject Category:Class_field_theory.
- Langlands_dual_group subject Category:Representation_theory_of_Lie_groups.
- Langlands_dual_group hypernym Group.
- Langlands_dual_group type Band.
- Langlands_dual_group type Thing.
- Langlands_dual_group comment "In representation theory, a branch of mathematics, the Langlands dual LG of a reductive algebraic group G (also called the L-group of G) is a group that controls the representation theory of G. If G is defined over a field k, then LG is an extension of the absolute Galois group of k by a complex Lie group. There is also a variation called the Weil form of the L-group, where the Galois group is replaced by a Weil group.".
- Langlands_dual_group label "Langlands dual group".
- Langlands_dual_group differentFrom Langlands_group.
- Langlands_dual_group sameAs ラングランズ双対.
- Langlands_dual_group sameAs 랭글랜즈_쌍대군.
- Langlands_dual_group sameAs m.0gp05h.
- Langlands_dual_group sameAs Q6486188.
- Langlands_dual_group sameAs Q6486188.
- Langlands_dual_group wasDerivedFrom Langlands_dual_group?oldid=638730958.
- Langlands_dual_group isPrimaryTopicOf Langlands_dual_group.