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A key application is in parabolic induction, which leads to the Langlands program: if is a reductive algebraic group and is the Langlands decomposition of a parabolic subgroup P, then parabolic induction consists of taking a representation of , extending it to by letting act trivially, and inducing the result from to .
langlands, decomposition, this, article, multiple, issues, please, help, improve, discuss, these, issues, talk, page, learn, when, remove, these, template, messages, this, article, relies, largely, entirely, single, source, relevant, discussion, found, talk, p. This article has multiple issues Please help improve it or discuss these issues on the talk page Learn how and when to remove these template messages This article relies largely or entirely on a single source Relevant discussion may be found on the talk page Please help improve this article by introducing citations to additional sources Find sources Langlands decomposition news newspapers books scholar JSTOR September 2021 This article includes a list of references related reading or external links but its sources remain unclear because it lacks inline citations Please help to improve this article by introducing more precise citations September 2021 Learn how and when to remove this template message Learn how and when to remove this template message In mathematics the Langlands decomposition writes a parabolic subgroup P of a semisimple Lie group as a product P M A N displaystyle P MAN of a reductive subgroup M an abelian subgroup A and a nilpotent subgroup N Contents 1 Applications 2 See also 3 References 3 1 SourcesApplications editSee also Parabolic induction A key application is in parabolic induction which leads to the Langlands program if G displaystyle G nbsp is a reductive algebraic group and P M A N displaystyle P MAN nbsp is the Langlands decomposition of a parabolic subgroup P then parabolic induction consists of taking a representation of M A displaystyle MA nbsp extending it to P displaystyle P nbsp by letting N displaystyle N nbsp act trivially and inducing the result from P displaystyle P nbsp to G displaystyle G nbsp See also editLie group decompositionsReferences editSources edit A W Knapp Structure theory of semisimple Lie groups ISBN 0 8218 0609 2 nbsp This mathematical analysis related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Langlands decomposition amp oldid 1194807368, wikipedia, wiki, book, books, library,
