Kazhdan-Lusztig conjecture
imported>Pythagoras0님의 2014년 8월 30일 (토) 02:48 판
introduction
- 1979 conjectures
- KL character formula
- KL positivity conjecture
- Kazhdan-Lusztig polynomial
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