en>Monkbot: Task 2: Fix CS1 deprecated coauthor parameter errors

2014-07-18T11:49:36Z

Task 2: Fix CS1 deprecated coauthor parameter errors

← Older revision		Revision as of 13:49, 18 July 2014
Line 1:		Line 1:
	~~The '''Isotypic component''' of weight <math>\lambda</math> of a Lie algebra module is the sum of all submodules which are isomorphic to the highest weight module with weight <math>\lambda</math>.~~

	~~==Definition==~~

	* A finite dimensional [[Module (mathematics)\|module]] <~~math~~>V<~~/math~~> ~~of a [[reductive Lie algebra]]~~ <~~math~~>~~\mathfrak{g}~~<~~/math~~> ~~(or of the corresponding [[Lie group]])~~ can be ~~decomposed into [[Irreducible representation\|irreducible]] submodules~~		Title: <br>5 Ways to Make Your BBQ a Memorable Family Event<br><br>Word Count:<br>517<br><br>Summary:<br>Every barbecue can and should be an exciting family event. 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	:<~~math~~> ~~V = \oplus_{i=1}^N V_i~~ </~~math~~>.
	* Each finite dimensional irreducible representation of <~~math~~>~~\mathfrak{g}~~<~~/math~~> ~~is uniquely identified (up to isomorphism) by its~~ [~~[Weight_(representation_theory)#Highest_weight\|highest weight~~]]
	:<~~math~~>~~\forall i \in \{1,\ldots,N\} \exists \lambda \in P(\mathfrak{g}) : V_i \simeq M_\lambda~~<~~/math~~>~~, where~~ <~~math~~>~~M_\lambda~~<~~/math~~> ~~denotes the [[Weight_(representation_theory)#Highest_weight_module\|highest weight module]] with highest weight~~ <~~math~~>~~\lambda~~<~~/math~~>.
	* In the decomposition of <~~math~~> V <~~/math~~>~~, a certain isomorphism class might appear more than once, hence~~
	:<~~math~~> ~~V \simeq \oplus_{\lambda \in P(\mathfrak{g})} ( \oplus_{i=1}^{d_\lambda} M_{\lambda})~~ <~~/math~~>.

	~~This defines the isotypic component of weight~~ <~~math~~>~~\lambda~~<~~/math~~> ~~of V:~~
	<~~math~~>~~\lambda(V) := \oplus_{i=1}^{d_\lambda} V_i \simeq \mathbb{C}^{d_\lambda} \otimes M_{\lambda}~~<~~/math~~> ~~where~~ <~~math~~>~~d_\lambda~~</~~math> is maximal~~.

	~~==See also==~~
	* [[Lie algebra representation]]
	* [~~[Weight (representation theory)]]~~

	~~== References ==~~
	* {{Cite journal
	~~\| doi = 10~~.~~1016~~/~~j.jalgebra.2010~~.~~10.031~~
	~~\| issn = 0021-8693~~
	~~\| volume = 328~~
	~~\| issue = 1~~
	~~\| pages = 322–329~~
	~~\| last = Bürgisser~~
	~~\| first = Peter~~
	~~\| coauthors = Matthias Christandl~~, ~~Christian Ikenmeyer~~
	~~\| title = Even partitions~~ in ~~plethysms~~
	~~\| journal = Journal~~ of ~~Algebra~~
	~~\| accessdate = 2011-03-26~~
	~~\| date = 2011-02-15~~
	~~\| url =~~ http://www.~~sciencedirect~~.~~com~~/~~science~~/~~article/B6WH2-51JTYBD~~-1/2~~/4f609599c6fff11261c5d5272c78e274~~
	}}

	* {{Cite journal
	~~\| doi = 10~~.~~1007/s00220~~-~~005~~-~~1330-9~~
	~~\| last = Heinzner~~
	~~\| first = P~~.
	~~\| coauthors =~~ A. ~~Huckleberry~~, M. ~~R Zirnbauer~~
	~~\| title = Symmetry classes~~ of ~~disordered fermions~~
	~~\| date = 2004-11-10~~
	~~\| arxiv = math-ph~~/~~0411040~~
	}}

	<!~~--- Categories ---~~>

	~~[[Category:Representation theory~~ of ~~Lie algebras]]~~
	~~[[Category:Articles created via~~ the ~~Article Wizard]]~~

en>Yobot: /* Relationship to pattern recognition */WP:CHECKWIKI errors fixed + general fixes using AWB (8961)

2013-02-28T16:42:55Z

Relationship to pattern recognition: WP:CHECKWIKI errors fixed + general fixes using AWB (8961)

← Older revision		Revision as of 18:42, 28 February 2013
Line 1:		Line 1:
	~~Hello from Brazil. I~~'~~m glad tօ camе here~~. ~~Μy first name іs Geraldine~~. <br>~~I live~~ in a ~~town called Guarapari іn western Brazil.~~<br>~~І was also born~~ in ~~Guarapari 28 yеars ago. Married іn February 2012~~. ~~ӏ'm woгking at~~ the ~~university.~~<br><br>~~mу web-site~~ ... [http://~~brookebeveridge~~.~~wordpress~~.com/~~2014~~/09/20/~~five~~-~~easy~~-~~steps~~-to-a-~~winning~~-~~rhinoplasty~~-~~pictures~~-~~after~~-~~surgery~~-~~strategy/ weight loss meal plans women~~]		The '''Isotypic component''' of weight <math>\lambda</math> of a Lie algebra module is the sum of all submodules which are isomorphic to the highest weight module with weight <math>\lambda</math>.

			==Definition==

			* A finite dimensional [[Module (mathematics)\|module]] <math>V</math> of a [[reductive Lie algebra]] <math>\mathfrak{g}</math> (or of the corresponding [[Lie group]]) can be decomposed into [[Irreducible representation\|irreducible]] submodules
			:<math> V = \oplus_{i=1}^N V_i </math>.
			* Each finite dimensional irreducible representation of <math>\mathfrak{g}</math> is uniquely identified (up to isomorphism) by its [[Weight_(representation_theory)#Highest_weight\|highest weight]]
			:<math>\forall i \in \{1,\ldots,N\} \exists \lambda \in P(\mathfrak{g}) : V_i \simeq M_\lambda</math>, where <math>M_\lambda</math> denotes the [[Weight_(representation_theory)#Highest_weight_module\|highest weight module]] with highest weight <math>\lambda</math>.
			* In the decomposition of <math> V </math>, a certain isomorphism class might appear more than once, hence
			:<math> V \simeq \oplus_{\lambda \in P(\mathfrak{g})} ( \oplus_{i=1}^{d_\lambda} M_{\lambda}) </math>.

			This defines the isotypic component of weight <math>\lambda</math> of V:
			<math>\lambda(V) := \oplus_{i=1}^{d_\lambda} V_i \simeq \mathbb{C}^{d_\lambda} \otimes M_{\lambda}</math> where <math>d_\lambda</math> is maximal.

			==See also==
			* [[Lie algebra representation]]
			* [[Weight (representation theory)]]

			== References ==
			* {{Cite journal
			\| doi = 10.1016/j.jalgebra.2010.10.031
			\| issn = 0021-8693
			\| volume = 328
			\| issue = 1
			\| pages = 322–329
			\| last = Bürgisser
			\| first = Peter
			\| coauthors = Matthias Christandl, Christian Ikenmeyer
			\| title = Even partitions in plethysms
			\| journal = Journal of Algebra
			\| accessdate = 2011-03-26
			\| date = 2011-02-15
			\| url = http://www.sciencedirect.com/science/article/B6WH2-51JTYBD-1/2/4f609599c6fff11261c5d5272c78e274
			}}

			* {{Cite journal
			\| doi = 10.1007/s00220-005-1330-9
			\| last = Heinzner
			\| first = P.
			\| coauthors = A. Huckleberry, M. R Zirnbauer
			\| title = Symmetry classes of disordered fermions
			\| date = 2004-11-10
			\| arxiv = math-ph/0411040
			}}

			<!--- Categories --->

			[[Category:Representation theory of Lie algebras]]
			[[Category:Articles created via the Article Wizard]]

198.164.42.71 at 12:24, 23 September 2011

2011-09-23T12:24:57Z

New page

Hello from Brazil. I'm glad tօ camе here. Μy first name іs Geraldine. <br>I live in a town called Guarapari іn western Brazil.<br>І was also born in Guarapari 28 yеars ago. Married іn February 2012. ӏ'm woгking at the university.<br><br>mу web-site ... [http://brookebeveridge.wordpress.com/2014/09/20/five-easy-steps-to-a-winning-rhinoplasty-pictures-after-surgery-strategy/ weight loss meal plans women]

Multicriteria classification - Revision history

en>Monkbot: Task 2: Fix CS1 deprecated coauthor parameter errors

en>Yobot: /* Relationship to pattern recognition */WP:CHECKWIKI errors fixed + general fixes using AWB (8961)

198.164.42.71 at 12:24, 23 September 2011