"Bruhat decomposition"의 두 판 사이의 차이
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<h5>realization of finite type cluster algebra</h5> | <h5>realization of finite type cluster algebra</h5> | ||
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| + | Yang, Shih-Wei, 와/과Andrei Zelevinsky. 2008. “Cluster algebras of finite type via Coxeter elements and principal minors”. <em>0804.3303</em> (4월 21). http://arxiv.org/abs/0804.3303. | ||
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\mathbb{C}[L^{c,c^{-1}}] is a cluster algebra of finite type. It has the same type as Cartan matrix. | \mathbb{C}[L^{c,c^{-1}}] is a cluster algebra of finite type. It has the same type as Cartan matrix. | ||
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| + | *remark | ||
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| + | x_{[i,j]} corresponds to the diagonal between i and j in the triangulation of regular (n+3)-gon | ||
2011년 4월 22일 (금) 05:33 판
introduction
double Bruhat cells
Bruhat order
Weyl group action
The decomposition of G into strata G^{u,v} is 'good with respect to total positivity.
realization of finite type cluster algebra
Yang, Shih-Wei, 와/과Andrei Zelevinsky. 2008. “Cluster algebras of finite type via Coxeter elements and principal minors”. 0804.3303 (4월 21). http://arxiv.org/abs/0804.3303.
\mathbb{C}[L^{c,c^{-1}}] is a cluster algebra of finite type. It has the same type as Cartan matrix.
type A_{n}
(i) inite seed is given by x=(x_{[1,1]},\cdots,x_{[1,n]}), y=(y_1,\cdots,y_n), B=B(C)
(ii) The set of cluster variables is \{x_{[i,j]}|1\leq i\leq j\leq n \}
(iii) The exchange relations
x_{[i,k]}x_{[j,l]} = y_{j-1}y_{j}\cdots y_{k} x_{[i,j-2]}jx_{[i,j-2]}+x_{[i,l]}x_{[j,l]} for 1\leq i\leq j-1\leq k\leq l-1\leq n
- remark
x_{[i,j]} corresponds to the diagonal between i and j in the triangulation of regular (n+3)-gon
example
history
encyclopedia
- http://en.wikipedia.org/wiki/Longest_element_of_a_Coxeter_group
- http://eom.springer.de/b/b017690.htm
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/[1]
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
expositions
- http://www-math.mit.edu/~gyuri/papers/bru1.pdf
- http://math.ucr.edu/home/baez/week186.html
- http://www.math.harvard.edu/~ryanr/bruhat_row-reduction.pdf
articles
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
- http://mathoverflow.net/questions/15438/a-slick-proof-of-the-bruhat-decomposition-for-gl-nk
- http://mathoverflow.net/questions/28569/is-there-a-morse-theory-proof-of-the-bruhat-decomposition
- http://mathoverflow.net/search?q=
- http://mathoverflow.net/search?q=
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field