"Bruhat decomposition"의 두 판 사이의 차이

2011년 4월 22일 (금) 05:22 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.

\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

@@ 14번째 줄: / 14번째 줄: @@
+<h5>realization of finite type cluster algebra</h5>
+\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