Block type symmetry of bigraded Toda hierarchy
Block type symmetry of bigraded Toda hierarchy
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DOI：
10.1063/1.3681205
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发表时间：
2012-01
影响因子：
1.3
通讯作者：
Chuanzhong Li;Jingsong He;Yu-cai Su
中科院分区：
文献类型：
--
作者：
Chuanzhong Li;Jingsong He;Yu-cai Su
在本文中，我们定义了Orlov-Schulman算子ML、MR，然后使用它们来构造二分级Toda层次结构的附加对称性。我们进一步表明，这些额外的对称性形成了一个有趣的无限维李代数，称为块型李代数，其结构理论和表示理论最近在文献中受到了广泛关注。通过在弱 W 约束下作用于两个不同的空间，我们特别发现了此块类型李代数的两种表示。
In this paper, we define Orlov-Schulman's operators ML, MR, and then use them to construct the additional symmetries of the bigraded Toda hierarchy. We further show that these additional symmetries form an interesting infinite-dimensional Lie algebra known as a Block type Lie algebra, whose structure theory and representation theory have recently received much attention in the literature. By acting on two different spaces under the weak W-constraints, we find in particular two representations of this Block type Lie algebra.