Drinfeld和Heisenberg双重子的弱分裂
Weak splittings of quotients of Drinfeld and Heisenberg doubles
摘要：
研究了Poisson齐性空间的单态叶理的精细结构。证明了Heisenberg和Drinfeld双的满射Poisson浸入的弱分裂的两个一般结果。这些结果的含义是，环面轨道的辛叶的对偶可以明确实现为Poisson-Dirac子流形的环面轨道的双打。结果有广泛的应用到许多家庭的真正的和复杂的泊松结构的旗品种。他们的环面轨道叶恢复重要的家庭的品种，如开放理查森品种。
英文摘要：
We investigate the fine structure of the simplectic foliations of Poisson homogeneous spaces. Two general results are proved for weak splittings of surjective Poisson submersions from Heisenberg and Drinfeld doubles. The implications of these results are that the torus orbits of symplectic leaves of the quotients can be explicitly realized as Poisson-Dirac submanifolds of the torus orbits of the doubles. The results have a wide range of applications to many families of real and complex Poisson structures on flag varieties. Their torus orbits of leaves recover important families of varieties such as the open Richardson varieties.
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