"Bruhat ordering"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 4번째 줄: | 4번째 줄: | ||
Define a partial order on the elements of $W$ as follows : | Define a partial order on the elements of $W$ as follows : | ||
| − | + | $u < v$ whenever $u = t v$ for some reflection $t$ and $\ell(u) < \ell(v)$. | |
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* example : http://groupprops.subwiki.org/wiki/File:Bruhatons3.png | * example : http://groupprops.subwiki.org/wiki/File:Bruhatons3.png | ||
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| + | ;thm | ||
| + | Given $x,y\in W$, we have $x<y$ in the Bruhat order if and only if there is a reduced expression $y=s_{i_1}s_{i_2}\cdots s_{i_k}$ such that $x$ can be written as a product of some of the $s_{i_j}$ in the same order as they appear in $y$. | ||
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| + | ==computational resource== | ||
| + | * https://drive.google.com/file/d/0B8XXo8Tve1cxdko1Z0hPZUNhZTQ/view | ||
2016년 5월 2일 (월) 06:37 판
- Let $W$ be a Coxeter group
- def (Bruhat ordering)
Define a partial order on the elements of $W$ as follows :
$u < v$ whenever $u = t v$ for some reflection $t$ and $\ell(u) < \ell(v)$.
- thm
Given $x,y\in W$, we have $x<y$ in the Bruhat order if and only if there is a reduced expression $y=s_{i_1}s_{i_2}\cdots s_{i_k}$ such that $x$ can be written as a product of some of the $s_{i_j}$ in the same order as they appear in $y$.