"Kazhdan-Lusztig conjecture"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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* hard Lefshetz theorem | * hard Lefshetz theorem | ||
* Hodge-Riemann bilinear relation | * Hodge-Riemann bilinear relation | ||
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| + | ==related items== | ||
| + | * [[Enumerative problems and Schubert calculus]] | ||
| + | * [[Flag manifold and flag variety]] | ||
2013년 12월 9일 (월) 08:01 판
introduction
- 1979 conjectures
- KL character formula
- KL positivity conjecture
Hecke algebra
- 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