"Kazhdan-Lusztig conjecture"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 1번째 줄: | 1번째 줄: | ||
==introduction== | ==introduction== | ||
| − | * character formula | + | * 1979 conjectures |
| − | * positivity conjecture | + | ** 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 | ||
| + | |||
==exposition== | ==exposition== | ||
* [https://docs.google.com/file/d/0B8XXo8Tve1cxd2JGOUFfSG5nbjQ/edit Williamson- Kazhdan-Lusztig conjecture and shadows of Hodge theory] | * [https://docs.google.com/file/d/0B8XXo8Tve1cxd2JGOUFfSG5nbjQ/edit Williamson- Kazhdan-Lusztig conjecture and shadows of Hodge theory] | ||
[[분류:Hecke algebra]] | [[분류:Hecke algebra]] | ||
2013년 5월 30일 (목) 13:21 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