Factorization Dynamics and Coxeter--Toda Lattices
Factorization Dynamics and Coxeter--Toda Lattices
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因式分解动力学和 Coxeter--Toda 格
DOI：
10.1007/s002200000212
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发表时间：
1999
影响因子：
2.4
通讯作者：
N. Reshetikhin
中科院分区：
文献类型：
--
作者：
T. Hoffmann;J. Kellendonk;N. Kutz;N. Reshetikhin
证明了具有标准Poisson Lie结构的单李群在Coxeter辛叶上的因式分解关系给出了一个可积动力系统。该系统可以看作是户田流的离散化。在SL n的情况下，因子分解动力学的积分是相对论性户田系统的积分。相当大的一部分文件是专门描述辛叶在简单的复杂李群，其Borel子群和他们的双打。
It is shown that the factorization relation on simple Lie groups with standard Poisson Lie structure restricted to Coxeter symplectic leaves gives an integrable dynamical system. This system can be regarded as a discretization of the Toda flow. In case ofSLnthe integrals of the factorization dynamics are integrals of the relativistic Toda system. A substantial part of the paper is devoted to the description of symplectic leaves in simple complex Lie groups, its Borel subgroups and their doubles.