"Cartan datum"의 두 판 사이의 차이

2012년 7월 23일 (월) 08:18 판

\(A=(a_{ij})_{i,j\in I}\) GCM
\(P^{\vee}=(\bigoplus_{i\in I}\mathbb{Z}h_{i})\bigoplus(\bigoplus_{j=1}^{\operatorname{corank}(A)}\mathbb{Z}d_{j})\) : dual weight lattice
\(\mathfrak{h}=\mathbb{Q}\otimes_{\mathbb{Z}} P^{\vee}\)
\(P=\{\lambda\in\mathfrak{h}^{*}|\lambda(P^{\vee})\subset \mathbb{Z}\}\) : weight lattice
\(\Pi^{\vee}=\{h_{i}|i\in I\}\) : simple coroots
\(\Pi=\{\alpha_{i}\in\mathfrak{h}^{*}|i\in \alpha_{i}(h_j}=a_{ji}\}\) : simple coroots

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+* <math>A=(a_{ij})_{i,j\in I}</math> GCM
+* <math>P^{\vee}=(\bigoplus_{i\in I}\mathbb{Z}h_{i})\bigoplus(\bigoplus_{j=1}^{\operatorname{corank}(A)}\mathbb{Z}d_{j})</math> : dual weight lattice
+* <math>\mathfrak{h}=\mathbb{Q}\otimes_{\mathbb{Z}} P^{\vee}</math>
+* <math>P=\{\lambda\in\mathfrak{h}^{*}|\lambda(P^{\vee})\subset \mathbb{Z}\}</math> : weight lattice
+* <math>\Pi^{\vee}=\{h_{i}|i\in I\}</math> : simple coroots
+* <math>\Pi=\{\alpha_{i}\in\mathfrak{h}^{*}|i\in \alpha_{i}(h_j}=a_{ji}\}</math> : simple coroots