"Kazhdan-Lusztig conjecture"의 두 판 사이의 차이

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-==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]]

"Kazhdan-Lusztig conjecture"의 두 판 사이의 차이

2020년 11월 14일 (토) 00:56 판

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