Kazhdan-Lusztig conjecture - 편집 역사

2021년 2월 17일 (수) 09:07에 Pythagoras0님의 편집

2021-02-17T09:07:00Z

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-26T13:58:00Z

메타데이터: 새 문단

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

2020-11-16T18:07:13Z

2020년 11월 16일 (월) 17:57에 Pythagoras0님의 편집

2020-11-16T17:57:57Z

2020년 11월 14일 (토) 08:56에 imported>Pythagoras0님의 편집

2020-11-14T08:56:07Z

2020년 11월 14일 (토) 08:56에 imported>Pythagoras0님의 편집

2020-11-14T08:56:07Z

imported>Pythagoras0: /* Hecke algebra */

2016-05-03T06:20:18Z

Hecke algebra

2016년 3월 18일 (금) 04:17에 imported>Pythagoras0님의 편집

2016-03-18T04:17:35Z

2014년 8월 30일 (토) 10:48에 imported>Pythagoras0님의 편집

2014-08-30T10:48:51Z

2014년 6월 11일 (수) 22:13에 imported>Pythagoras0님의 편집

2014-06-11T22:13:16Z

@@ 43번째 줄: / 43번째 줄: @@
 [[분류:migrate]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q6381065 Q6381065]

← 이전 판		2020년 12월 26일 (토) 13:58 판
42번째 줄:		42번째 줄:
	[[분류:Hecke algebra]]		[[분류:Hecke algebra]]
	[[분류:migrate]]		[[분류:migrate]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q6381065 Q6381065]

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
-* The Kazhdan-Lusztig theory provides the solution to the problem of determining the irreducible characters in the  BGG category $\mathcal{O}$ of semisimple Lie algebras ([KL], [BB], [BK]).
+* The Kazhdan-Lusztig theory provides the solution to the problem of determining the irreducible characters in the  BGG category <math>\mathcal{O}</math> of semisimple Lie algebras ([KL], [BB], [BK]).
 * The theory was originally formulated in terms of the canonical bases (i.e., Kazhdan-Lusztig bases) of Hecke algebras.
 * 1979 conjectures
@@ 10번째 줄: / 10번째 줄: @@
 ==Hecke algebra==
-* basis of Hecke algebra $\{H_{x}| x\in W\}$
+* basis of Hecke algebra <math>\{H_{x}| x\in W\}</math>
-* new basis of Hecke algebra $\{\underline{H}_{x}| x\in W\}$
+* new basis of Hecke algebra <math>\{\underline{H}_{x}| x\in W\}</math>
-$$
+:<math>
 \underline{H}_{x}=H_{x}+\sum_{y\in W, \ell(y)<\ell(x)} h_{y,x}H_{y}
-$$
+</math>
-where $h_{y,x}\in v\mathbb{Z}[v]$ is so called the Kazhdan-Lusztig polynomial
+where <math>h_{y,x}\in v\mathbb{Z}[v]</math> is so called the Kazhdan-Lusztig polynomial
-* positivity conjecture : $h_{x,y}\in \mathbb{Z}_{\geq 0}[v]$
+* positivity conjecture : <math>h_{x,y}\in \mathbb{Z}_{\geq 0}[v]</math>
 ==Hodge theory==
@@ 36번째 줄: / 36번째 줄: @@
 ==articles==
-* [BB] A. Beilinson and J. Bernstein, Localisation de $\mathfrak g$-modules, C.R. Acad. Sci. Paris Ser. I Math. 292 (1981), 15-18.
+* [BB] A. Beilinson and J. Bernstein, Localisation de <math>\mathfrak g</math>-modules, C.R. Acad. Sci. Paris Ser. I Math. 292 (1981), 15-18.
 * [BK] J.L.Brylinski and M.Kashiwara, Kazhdan-Lusztig conjecture and holonomic systems, Invent. Math. 64 (1981), 387-410.
 * [KL] D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165-184.

← 이전 판	2020년 11월 14일 (토) 08:56 판
1번째 줄:	1번째 줄:
	+	==introduction==
	+	* The Kazhdan-Lusztig theory provides the solution to the problem of determining the irreducible characters in the BGG category $\mathcal{O}$ of semisimple Lie algebras ([KL], [BB], [BK]).
	+	* The theory was originally formulated in terms of the canonical bases (i.e., Kazhdan-Lusztig bases) of Hecke algebras.
	+	* 1979 conjectures
	+	** KL character formula
	+	** KL positivity conjecture
	+	* [[Kazhdan-Lusztig polynomial]]

	+
	+
	+	==Hecke algebra==
	+	* basis of Hecke algebra $\{H_{x}\| x\in W\}$
	+	* new basis of Hecke algebra $\{\underline{H}_{x}\| x\in W\}$
	+	$$
	+	\underline{H}_{x}=H_{x}+\sum_{y\in W, \ell(y)<\ell(x)} h_{y,x}H_{y}
	+	$$
	+	where $h_{y,x}\in v\mathbb{Z}[v]$ is so called the Kazhdan-Lusztig polynomial
	+	* positivity conjecture : $h_{x,y}\in \mathbb{Z}_{\geq 0}[v]$
	+
	+	==Hodge theory==
	+	* Poincare duality
	+	* hard Lefshetz theorem
	+	* Hodge-Riemann bilinear relation
	+
	+
	+	==related items==
	+	* [[BGG category]]
	+	* [[Hecke algebra]]
	+	* [[Enumerative problems and Schubert calculus]]
	+	* [[Flag manifold and flag variety]]
	+
	+
	+	==exposition==
	+	* [https://docs.google.com/file/d/0B8XXo8Tve1cxd2JGOUFfSG5nbjQ/edit Williamson- Kazhdan-Lusztig conjecture and shadows of Hodge theory]
	+
	+
	+	==articles==
	+	* [BB] A. Beilinson and J. Bernstein, Localisation de $\mathfrak g$-modules, C.R. Acad. Sci. Paris Ser. I Math. 292 (1981), 15-18.
	+	* [BK] J.L.Brylinski and M.Kashiwara, Kazhdan-Lusztig conjecture and holonomic systems, Invent. Math. 64 (1981), 387-410.
	+	* [KL] D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165-184.
	+
	+	[[분류:Hecke algebra]]
	+	[[분류:migrate]]

← 이전 판		2020년 11월 14일 (토) 08:56 판
1번째 줄:		1번째 줄:
−	~~==introduction==~~
−	* The Kazhdan-Lusztig theory provides the solution to the problem of determining the irreducible characters in the BGG category $\mathcal{O}$ of semisimple Lie algebras ([KL], [BB], [BK]).
−	* The theory was originally formulated in terms of the canonical bases (i.e., Kazhdan-Lusztig bases) of Hecke algebras.
−	* 1979 conjectures
−	** KL character formula
−	** KL positivity conjecture
−	* [[Kazhdan-Lusztig polynomial]]

−
−
−	~~==Hecke algebra==~~
−	* basis of Hecke algebra $\{H_{x}\| x\in W\}$
−	* new basis of Hecke algebra $\{\underline{H}_{x}\| x\in W\}$
−	$$
−	~~\underline{H}_{x}=H_{x}+\sum_{y\in W, \ell(y)<\ell(x)} h_{y,x}H_{y}~~
−	$$
−	~~where $h_{y,x}\in v\mathbb{Z}[v]$ is so called the Kazhdan-Lusztig polynomial~~
−	* positivity conjecture : $h_{x,y}\in \mathbb{Z}_{\geq 0}[v]$
−
−	~~==Hodge theory==~~
−	* Poincare duality
−	* hard Lefshetz theorem
−	* Hodge-Riemann bilinear relation
−
−
−	~~==related items==~~
−	* [[BGG category]]
−	* [[Hecke algebra]]
−	* [[Enumerative problems and Schubert calculus]]
−	* [[Flag manifold and flag variety]]
−
−
−	~~==exposition==~~
−	* [https://docs.google.com/file/d/0B8XXo8Tve1cxd2JGOUFfSG5nbjQ/edit Williamson- Kazhdan-Lusztig conjecture and shadows of Hodge theory]
−
−
−	~~==articles==~~
−	* [BB] A. Beilinson and J. Bernstein, Localisation de $\mathfrak g$-modules, C.R. Acad. Sci. Paris Ser. I Math. 292 (1981), 15-18.
−	* [BK] J.L.Brylinski and M.Kashiwara, Kazhdan-Lusztig conjecture and holonomic systems, Invent. Math. 64 (1981), 387-410.
−	* [KL] D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165-184.
−
−	~~[[분류:Hecke algebra]]~~

← 이전 판	2020년 11월 16일 (월) 17:57 판
(차이 없음)

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
 * 1979 conjectures
 ** KL character formula
 ** KL positivity conjecture
 * [[Kazhdan-Lusztig polynomial]]
@@ 23번째 줄: / 26번째 줄: @@
 ==related items==
 * [[Hecke algebra]]
 * [[Enumerative problems and Schubert calculus]]
@@ 30번째 줄: / 34번째 줄: @@
 ==exposition==
 * [https://docs.google.com/file/d/0B8XXo8Tve1cxd2JGOUFfSG5nbjQ/edit Williamson- Kazhdan-Lusztig conjecture and shadows of Hodge theory]
 [[분류:Hecke algebra]]

← 이전 판		2014년 8월 30일 (토) 10:48 판
3번째 줄:		3번째 줄:
	** KL character formula		** KL character formula
	** KL positivity conjecture		** KL positivity conjecture
		+	* [[Kazhdan-Lusztig polynomial]]