Springer correspondence - 편집 역사

2021년 2월 17일 (수) 09:01에 Pythagoras0님의 편집

2021-02-17T09:01:58Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-26T13:40:29Z

메타데이터: 새 문단

2020년 11월 16일 (월) 18:10에 Pythagoras0님의 편집

2020-11-16T18:10:37Z

2020년 11월 16일 (월) 18:07에 Pythagoras0님의 편집

2020-11-16T18:07:54Z

2020년 11월 16일 (월) 11:29에 imported>Pythagoras0님의 편집

2020-11-16T11:29:52Z

2020년 11월 16일 (월) 11:29에 imported>Pythagoras0님의 편집

2020-11-16T11:29:52Z

imported>Pythagoras0: /* introduction */

2017-03-21T02:45:31Z

introduction

imported>Pythagoras0: /* introduction */

2017-03-21T02:44:02Z

introduction

imported>Pythagoras0: /* articles */

2017-03-21T02:30:25Z

articles

imported>Pythagoras0: /* articles */

2017-03-21T02:29:58Z

articles

@@ 37번째 줄: / 37번째 줄: @@
 [[분류:migrate]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q7580874 Q7580874]

← 이전 판		2020년 12월 26일 (토) 13:40 판
36번째 줄:		36번째 줄:
	[[분류:Lie theory]]		[[분류:Lie theory]]
	[[분류:migrate]]		[[분류:migrate]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q7580874 Q7580874]

@@ 7번째 줄: / 7번째 줄: @@
 ==nilpotent variety==
-* Given a semisimple algebraic group $G$ with Lie algebra $\mathfrak{g}$, we call the closure of a $G$-orbit in the nilpotent elements of $\mathfrak{g}$ a nilpotent variety.
+* Given a semisimple algebraic group <math>G</math> with Lie algebra <math>\mathfrak{g}</math>, we call the closure of a <math>G</math>-orbit in the nilpotent elements of <math>\mathfrak{g}</math> a nilpotent variety.
 ==related items==

← 이전 판	2020년 11월 16일 (월) 11:29 판
1번째 줄:	1번째 줄:
	+	==introduction==
	+	* In his paper [Spr76], Springer defined a certain representation of the Weyl group of a reductive group on the cohomology of a set of fixed points in the flag variety by a nilpotent element, which we now call the Springer representation.
	+	* In particular, for various sets of such fixed points, called Springer fibers, the top degree cohomology gives all the irreducible representations of the corresponding Weyl group.
	+	* The Springer correspondence makes a link between the characters of a Weyl group and the geometry of the nilpotent cone of the corresponding semisimple Lie algebra
	+	* extend this to an equivalence between the triangulated category generated by the Springer perverse sheaves and the derived category of differential graded modules over a dg-ring related to the Weyl group

	+
	+	==nilpotent variety==
	+	* Given a semisimple algebraic group $G$ with Lie algebra $\mathfrak{g}$, we call the closure of a $G$-orbit in the nilpotent elements of $\mathfrak{g}$ a nilpotent variety.
	+
	+	==related items==
	+	* {{수학노트\|url=콕세터_군의_표현론}}
	+
	+
	+	==expositions==
	+	* Achar, Pramod N., Anthony Henderson, Daniel Juteau, and Simon Riche. “Modular Generalized Springer Correspondence: An Overview.” arXiv:1510.08962 [math], October 29, 2015. http://arxiv.org/abs/1510.08962.
	+	* Clausen, http://www.math.harvard.edu/theses/senior/clausen/clausen.pdf
	+
	+	==encyclopedia==
	+	* http://en.wikipedia.org/wiki/Nilpotent_cone
	+	* http://en.wikipedia.org/wiki/Springer_correspondence
	+
	+
	+	==articles==
	+	* Julianna Tymoczko, The geometry and combinatorics of Springer fibers, arXiv:1606.02760 [math.AG], June 08 2016, http://arxiv.org/abs/1606.02760
	+	* Aubert, Anne-Marie, Ahmed Moussaoui, and Maarten Solleveld. “Generalizations of the Springer Correspondence and Cuspidal Langlands Parameters.” arXiv:1511.05335 [math], November 17, 2015. http://arxiv.org/abs/1511.05335.
	+	* Chen, Tsao-Hsien, Kari Vilonen, and Ting Xue. “Hessenberg Varieties, Intersections of Quadrics, and the Springer Correspondence.” arXiv:1511.00617 [math], November 2, 2015. http://arxiv.org/abs/1511.00617.
	+	* Achar, Pramod N., Anthony Henderson, Daniel Juteau, and Simon Riche. “Modular Generalized Springer Correspondence III: Exceptional Groups.” arXiv:1507.00401 [math], July 1, 2015. http://arxiv.org/abs/1507.00401.
	+	* Juteau, Daniel. “Modular Springer Correspondence, Decomposition Matrices and Basic Sets.” arXiv:1410.1471 [math], October 6, 2014. http://arxiv.org/abs/1410.1471.
	+	* Rider, Laura, and Amber Russell. “Perverse Sheaves on the Nilpotent Cone and Lusztig’s Generalized Springer Correspondence.” arXiv:1409.7132 [math], September 24, 2014. http://arxiv.org/abs/1409.7132.
	+	* Rider, Laura. “Formality for the Nilpotent Cone and a Derived Springer Correspondence.” arXiv:1206.4343 [math], June 19, 2012. http://arxiv.org/abs/1206.4343.
	+	* Ciubotaru, Dan. “Spin Representations of Weyl Groups and the Springer Correspondence.” Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 2012, no. 671 (2011): 199–222. doi:10.1515/CRELLE.2011.160.
	+	* Springer, T.A.. "Trigonometric Sums, Green Functions on Finite Groups and Representation of Weyl Groups.." Inventiones mathematicae 36 (1976): 173-208
	+	** http://ams.mpim-bonn.mpg.de/mathscinet-getitem?mr=MR0442103
	+	[[분류:duality]]
	+	[[분류:Lie theory]]
	+	[[분류:migrate]]

← 이전 판		2020년 11월 16일 (월) 11:29 판
1번째 줄:		1번째 줄:
−	~~==introduction==~~
−	* In his paper [Spr76], Springer defined a certain representation of the Weyl group of a reductive group on the cohomology of a set of fixed points in the flag variety by a nilpotent element, which we now call the Springer representation.
−	* In particular, for various sets of such fixed points, called Springer fibers, the top degree cohomology gives all the irreducible representations of the corresponding Weyl group.
−	* The Springer correspondence makes a link between the characters of a Weyl group and the geometry of the nilpotent cone of the corresponding semisimple Lie algebra
−	* extend this to an equivalence between the triangulated category generated by the Springer perverse sheaves and the derived category of differential graded modules over a dg-ring related to the Weyl group

−
−	~~==nilpotent variety==~~
−	* Given a semisimple algebraic group $G$ with Lie algebra $\mathfrak{g}$, we call the closure of a $G$-orbit in the nilpotent elements of $\mathfrak{g}$ a nilpotent variety.
−
−	~~==related items==~~
−	* {{수학노트\|url=콕세터_군의_표현론}}
−
−
−	~~==expositions==~~
−	* Achar, Pramod N., Anthony Henderson, Daniel Juteau, and Simon Riche. “Modular Generalized Springer Correspondence: An Overview.” arXiv:1510.08962 [math], October 29, 2015. http://arxiv.org/abs/1510.08962.
−	* Clausen, http://www.math.harvard.edu/theses/senior/clausen/clausen.pdf
−
−	~~==encyclopedia==~~
−	* http://en.wikipedia.org/wiki/Nilpotent_cone
−	* http://en.wikipedia.org/wiki/Springer_correspondence
−
−
−	~~==articles==~~
−	* Julianna Tymoczko, The geometry and combinatorics of Springer fibers, arXiv:1606.02760 [math.AG], June 08 2016, http://arxiv.org/abs/1606.02760
−	* Aubert, Anne-Marie, Ahmed Moussaoui, and Maarten Solleveld. “Generalizations of the Springer Correspondence and Cuspidal Langlands Parameters.” arXiv:1511.05335 [math], November 17, 2015. http://arxiv.org/abs/1511.05335.
−	* Chen, Tsao-Hsien, Kari Vilonen, and Ting Xue. “Hessenberg Varieties, Intersections of Quadrics, and the Springer Correspondence.” arXiv:1511.00617 [math], November 2, 2015. http://arxiv.org/abs/1511.00617.
−	* Achar, Pramod N., Anthony Henderson, Daniel Juteau, and Simon Riche. “Modular Generalized Springer Correspondence III: Exceptional Groups.” arXiv:1507.00401 [math], July 1, 2015. http://arxiv.org/abs/1507.00401.
−	* Juteau, Daniel. “Modular Springer Correspondence, Decomposition Matrices and Basic Sets.” arXiv:1410.1471 [math], October 6, 2014. http://arxiv.org/abs/1410.1471.
−	* Rider, Laura, and Amber Russell. “Perverse Sheaves on the Nilpotent Cone and Lusztig’s Generalized Springer Correspondence.” arXiv:1409.7132 [math], September 24, 2014. http://arxiv.org/abs/1409.7132.
−	* Rider, Laura. “Formality for the Nilpotent Cone and a Derived Springer Correspondence.” arXiv:1206.4343 [math], June 19, 2012. http://arxiv.org/abs/1206.4343.
−	* Ciubotaru, Dan. “Spin Representations of Weyl Groups and the Springer Correspondence.” Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 2012, no. 671 (2011): 199–222. doi:10.1515/CRELLE.2011.160.
−	* Springer, T.A.. "Trigonometric Sums, Green Functions on Finite Groups and Representation of Weyl Groups.." Inventiones mathematicae 36 (1976): 173-208
−	** http://ams.mpim-bonn.mpg.de/mathscinet-getitem?mr=MR0442103
−	~~[[분류:duality]]~~
−	~~[[분류:Lie theory]]~~

← 이전 판	2020년 11월 16일 (월) 18:07 판
(차이 없음)

← 이전 판		2017년 3월 21일 (화) 02:45 판
5번째 줄:		5번째 줄:
	* extend this to an equivalence between the triangulated category generated by the Springer perverse sheaves and the derived category of differential graded modules over a dg-ring related to the Weyl group		* extend this to an equivalence between the triangulated category generated by the Springer perverse sheaves and the derived category of differential graded modules over a dg-ring related to the Weyl group

		+
		+	==nilpotent variety==
	* Given a semisimple algebraic group $G$ with Lie algebra $\mathfrak{g}$, we call the closure of a $G$-orbit in the nilpotent elements of $\mathfrak{g}$ a nilpotent variety.		* Given a semisimple algebraic group $G$ with Lie algebra $\mathfrak{g}$, we call the closure of a $G$-orbit in the nilpotent elements of $\mathfrak{g}$ a nilpotent variety.

@@ 30번째 줄: / 30번째 줄: @@
 * Ciubotaru, Dan. “Spin Representations of Weyl Groups and the Springer Correspondence.” Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 2012, no. 671 (2011): 199–222. doi:10.1515/CRELLE.2011.160.
 * Springer, T.A.. "Trigonometric Sums, Green Functions on Finite Groups and Representation of Weyl Groups.." Inventiones mathematicae 36 (1976): 173-208
+** http://ams.mpim-bonn.mpg.de/mathscinet-getitem?mr=MR0442103
 [[분류:duality]]
 [[분류:Lie theory]]