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==introduction== | ==introduction== | ||
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* Bruhat order | * Bruhat order | ||
* Weyl group action | * Weyl group action | ||
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* Double cosets <math>BwB</math> and <math>B_{-}wB_{-}</math> are called Bruhat cells. | * Double cosets <math>BwB</math> and <math>B_{-}wB_{-}</math> are called Bruhat cells. | ||
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==encyclopedia== | ==encyclopedia== | ||
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==expositions== | ==expositions== | ||
| − | + | * Lusztig, G. 2010. “Bruhat Decomposition and Applications.” arXiv:1006.5004 [math] (June 25). http://arxiv.org/abs/1006.5004. | |
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* http://math.ucr.edu/home/baez/week186.html | * http://math.ucr.edu/home/baez/week186.html | ||
| − | * http://www. | + | * [http://www.ryancreich.info/bruhat_row-reduction.pdf Bruhat decomposition via row reduction] |
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2013년 12월 7일 (토) 07:08 판
introduction
- Bruhat order
- Weyl group action
Bruhat cell
- $G=GL_{n}$
- $B$ : upper triangular matrices in $G$
- $B_{-}$ : lower triangular matrices in $G$
- $W=S_{n}$ we can think of it as a subgroup of $G$
- Double cosets \(BwB\) and \(B_{-}wB_{-}\) are called Bruhat cells.
memo
computational resource
encyclopedia
- http://en.wikipedia.org/wiki/Longest_element_of_a_Coxeter_group
- http://eom.springer.de/b/b017690.htm
expositions
- Lusztig, G. 2010. “Bruhat Decomposition and Applications.” arXiv:1006.5004 [math] (June 25). http://arxiv.org/abs/1006.5004.
- http://math.ucr.edu/home/baez/week186.html
- Bruhat decomposition via row reduction