"Bruhat decomposition"의 두 판 사이의 차이

2011년 7월 19일 (화) 15:38 판

double Bruhat cells

Bruhat order

Weyl group action

The decomposition of G into strata G^{u,v} is 'good with respect to total positivity.

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

x_{[i,j]} corresponds to the diagonal between i and j in the triangulation of regular (n+3)-gon

@@ 6번째 줄: / 6번째 줄: @@
 Weyl group action
+The decomposition of G into strata G^{u,v} is 'good with respect to total positivity.
-The decomposition of G into strata G^{u,v} is 'good with respect to total positivity.
+<h5>Bruhat</h5>
@@ 104번째 줄: / 108번째 줄: @@
 <h5>expositions</h5>
-* [http://www-math.mit.edu/%7Egyuri/papers/bru1.pdf http://www-math.mit.edu/~gyuri/papers/bru1.pdf]
+* [http://www-math.mit.edu/%7Egyuri/papers/bru1.pdf ][http://www-math.mit.edu/%7Egyuri/papers/bru1.pdf http://www-math.mit.edu/~gyuri/papers/bru1.pdf]
-* http://pages.uoregon.edu/dmoseley/talks/Lecture14.pdf
+* Double Bruhat Cells http://pages.uoregon.edu/dmoseley/talks/Lecture14.pdf
+* Cluster Structures on Double Bruhat Cells http://pages.uoregon.edu/dmoseley/talks/Lecture15.pdf
 * http://math.ucr.edu/home/baez/week186.html
 * [http://www.math.harvard.edu/%7Eryanr/bruhat_row-reduction.pdf http://www.math.harvard.edu/~ryanr/bruhat_row-reduction.pdf]