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2014-02-15T00:44:19Z

cleanup after paste/merger (style needs work)

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	In mathematics, the '''Langlands decomposition''' writes a [[parabolic subgroup]] ''P'' of a [[semisimple Lie group]] as a [[product of subgroups\|product]] <math>P=MAN</math> of a reductive subgroup ''M'', an [[abelian group\|abelian]] subgroup ''A'', and ~~a [[nilpotent group\|nilpotent subgroup]] ''N''~~.		Andrew Berryhill is what his spouse loves to contact him and he completely digs that title. Her family members lives in Ohio. Invoicing is my profession. To climb is some thing I truly appreciate performing.<br><br>Here is my blog: good psychic ([http://cpacs.org/index.php?document_srl=90091&mid=board_zTGg26 simply click the following internet page])

	~~== Applications ==~~
	~~{{see also\|Parabolic induction}}~~
	~~A key application~~ is ~~in [[parabolic induction]], which leads to the [[Langlands program]]: if <math>G</math>~~ is ~~a reductive algebraic group and~~ <~~math~~>~~P=MAN~~<~~/math~~> is ~~the Langlands decomposition of a parabolic subgroup ''P'', then~~ [~~[parabolic induction]] consists of taking a representation of <math>MA<~~/~~math>, extending it to <math>P<~~/~~math> by letting <math>N<~~/~~math> act trivially, and [[induced representation\|inducing]] the result from <math>P</math> to <math>G</math>~~.

	==~~See also==~~
	*[[Lie group decompositions]]

	~~==References==~~
	* A. W. Knapp, Structure theory of semisimple Lie groups. ISBN 0-8218-0609-2.

	~~{{DEFAULTSORT:Langlands Decomposition}}~~
	~~[[Category:Lie groups]]~~
	~~[[Category:Algebraic groups]~~]


	~~{{Mathanalysis-stub}}~~

en>Maxlittle2007: /* Nonexistent broken link fix. */

2010-11-30T00:53:27Z

Nonexistent broken link fix.

New page

In mathematics, the '''Langlands decomposition''' writes a [[parabolic subgroup]] ''P'' of a [[semisimple Lie group]] as a [[product of subgroups|product]] <math>P=MAN</math> of a reductive subgroup ''M'', an [[abelian group|abelian]] subgroup ''A'', and a [[nilpotent group|nilpotent subgroup]] ''N''.

== Applications ==
{{see also|Parabolic induction}}
A key application is in [[parabolic induction]], which leads to the [[Langlands program]]: if <math>G</math> is a reductive algebraic group and <math>P=MAN</math> is the Langlands decomposition of a parabolic subgroup ''P'', then [[parabolic induction]] consists of taking a representation of <math>MA</math>, extending it to <math>P</math> by letting <math>N</math> act trivially, and [[induced representation|inducing]] the result from <math>P</math> to <math>G</math>.

==See also==
*[[Lie group decompositions]]

==References==
* A. W. Knapp, Structure theory of semisimple Lie groups. ISBN 0-8218-0609-2.

{{DEFAULTSORT:Langlands Decomposition}}
[[Category:Lie groups]]
[[Category:Algebraic groups]]

{{Mathanalysis-stub}}

Maximum entropy spectral estimation - Revision history

en>GeoGreg: cleanup after paste/merger (style needs work)

en>Maxlittle2007: /* Nonexistent broken link fix. */