The trigonometric Casimir connection of a simple Lie algebra
The trigonometric Casimir connection of a simple Lie algebra
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简单李代数的三角卡西米尔连接
DOI：
10.1016/j.jalgebra.2010.05.025
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发表时间：
2011
影响因子：
0.9
通讯作者：
V. T. Laredo
中科院分区：
文献类型：
--
作者：
V. T. Laredo
设g是一个复半单李代数，g是相应的单连通李群，H∧g是一个极大环面。构造了H上具有根超环上的对数奇异点和g的Yangian Y(g)上的值的平面连接。通过类比g的有理Casimir连接，我们推测了这个三角连接的单性可以用量子环代数U (l)的量子Weyl群算子来描述。
Let g be a complex, semisimple Lie algebra, G the corresponding simply-connected Lie group and H⊂G a maximal torus. We construct a flat connection on H with logarithmic singularities on the root hypertori and values in the Yangian Y(g) of g. By analogy with the rational Casimir connection of g, we conjecture that the monodromy of this trigonometric connection is described by the quantum Weyl group operators of the quantum loop algebra Uℏ(Lg).