Calogero-Moser Lax pairs with spectral parameter for general Lie algebras
Calogero-Moser Lax pairs with spectral parameter for general Lie algebras
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一般李代数的带有谱参数的 Calogero-Moser Lax 对
DOI：
10.1016/s0550-3213(98)00568-9
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
D. Phong
中科院分区：
文献类型：
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作者：
E. D'hoker;E. D'hoker;D. Phong
我们构造了一个带谱参数的椭圆型Calogero-Moser哈密顿系统，该系统与每一个有限维李代数相关，具有经典型和例外型。当谱参数等于椭圆曲线的三个半周期之一时，我们的经典李代数的结果简化为先前已知的没有谱参数的Lax对之一。这些Calogero-Moser系统在相关的未扭曲仿射李代数的Weyl群下是不变的。对于非单列李代数，我们引入了新的与扭曲仿射李代数自然相关的可积系统，并构造了它们的带谱参数的Lax算子（G2除外）。
We construct a Lax pair with spectral parameter for the elliptic Calogero-Moser Hamiltonian systems associated with each of the finite-dimensional Lie algebras, of the classical and of the exceptional type. When the spectral parameter equals one of the three half periods of the elliptic curve, our result for the classical Lie algebras reduces to one of the Lax pairs without spectral parameter that were known previously. These Calogero-Moser systems are invariant under the Weyl group of the associated untwisted affine Lie algebra. For non-simply laced Lie algebras, we introduce new integrable systems, naturally associated with twisted affine Lie algebras, and construct their Lax operators with spectral parameter (except in the case of G2).