Toda lattice and toric varieties for real split semisimple Lie algebras
Toda lattice and toric varieties for real split semisimple Lie algebras
复制标题
实分裂半单李代数的 Toda 格子和环面簇
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
Y. Kodama
中科院分区：
文献类型：
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作者：
L. Casian;Y. Kodama
研究了与真实的分裂半单李代数相联系的一类Jacobi元的等谱真实的光滑流形的拓扑.该流形被定义为相应李群G的不连通Cartan子群的紧致连通完备化，该不连通Cartan子群是G的所有标准抛物子群的Levi因子的半单部分所对应的分裂Cartan子群的不交并.该流形还与定义在半单李代数上的广义户田格方程的紧化水平集有关，该格方程与具有Borel子群B的旗流形G/B中的环面簇同构.然后，我们给出了一个细胞分解和相关的链复杂的流形通过引入彩色签署Dynkin图参数化的细胞在分解。
The paper concerns the topology of an isospectral real smooth manifold for certain Jacobi element associated with real split semisimple Lie algebra. The manifold is identified as a compact, connected completion of the disconnected Cartan subgroup of the corresponding Lie group G which is a disjoint union of the split Cartan subgroups associated to semisimple portions of Levi factors of all standard parabolic subgroups of G. The manifold is also related to the compactifled level sets of a generalized Toda lattice equation defined on the semisimple Lie algebra, which is diffeomorphic to a toric variety in the flag manifold G/B with Borel subgroup B of G. We then give a cellular decomposition and the associated chain complex of the manifold by introducing colored-signed Dynkin diagrams which parametrize the cells in the decomposition.