Sp（2n，C）表示的Gel'fand-Cetlin-Molev基的辛几何
The symplectic geometry of the Gel'fand-Cetlin-Molev basis for representations of Sp(2n,C)
摘要：
Gel'fand和Cetlin在20世纪50年代构造了U（n，\C）的有限维表示V（λ）的规范基，通过子群链对表示进行连续分解。Guillemin和Sternberg在20世纪80年代构造了U（n，\C）的余伴随轨道上的Gel'fand-Cetlin可积系统，它是通过几何量子化的Gel'fand-Cetlin构造的辛几何版本。(Much相同的构造适用于SO（n，\R）的表示。A.莫列夫在1999年发现了一个用于表示辛群的盖尔范德-切特林型基，使用了本质上新的思想。一个重要的新角色是杨格数Y（2），一个无限维的霍普夫代数，以及Y（2）的一个称为扭曲杨格数Y^{-}（2）的子代数。本文利用形变理论对U（n，\H）给出了类似的辛几何结果，即在U（n，\H）的余伴轨道上构造了一个完全可积系统.我们称之为Gel'fand-Cetlin-Molev可积系统。
英文摘要：
Gel'fand and Cetlin constructed in the 1950s a canonical basis for a finite-dimensional representation V(λ) of U(n,\C) by successive decompositions of the representation by a chain of subgroups. Guillemin and Sternberg constructed in the 1980s the Gel'fand-Cetlin integrable system on the coadjoint orbits of U(n,\C), which is the symplectic geometric version, via geometric quantization, of the Gel'fand-Cetlin construction. (Much the same construction works for representations of SO(n,\R).) A. Molev in 1999 found a Gel'fand-Cetlin-type basis for representations of the symplectic group, using essentially new ideas. An important new role is played by the Yangian Y(2), an infinite-dimensional Hopf algebra, and a subalgebra of Y(2) called the twisted Yangian Y^{-}(2). In this paper we use deformation theory to give the analogous symplectic-geometric results for the case of U(n,\H), i.e. we construct a completely integrable system on the coadjoint orbits of U(n,\H). We call this the Gel'fand-Cetlin-Molev integrable system.
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