论文标题
Gelfand-Cetlin Abelianizatizations的Abelianization
Gelfand-Cetlin abelianizations of symplectic quotients
论文作者
论文摘要
我们表明，通过紧凑的连接谎言组$ g $的作用，哈密顿$ g $ g $ - 空间$ m $的通用符号符号也是紧凑型圆环的同一歧管$ m $的符号符号。所讨论的圆环动作来自$ \ mathfrak {g}^*$的某些集成系统，$ g $的Lie代数的双重。此类集成系统的示例包括在单一和特殊正交组的情况下，Gelfand-Cetlin系统的Gelfand-Cetlin系统，以及Hoffman-Lane为所有紧凑型连接的Lie组构建的某些可集成系统。我们的Abelianization的结果适用于光滑的商，而更普遍地是在Sjamaar-Lerman意义上是分层符号空间的商。
We show that generic symplectic quotients of a Hamiltonian $G$-space $M$ by the action of a compact connected Lie group $G$ are also symplectic quotients of the same manifold $M$ by a compact torus. The torus action in question arises from certain integrable systems on $\mathfrak{g}^*$, the dual of the Lie algebra of $G$. Examples of such integrable systems include the Gelfand-Cetlin systems of Guillemin-Sternberg in the case of unitary and special orthogonal groups, and certain integrable systems constructed for all compact connected Lie groups by Hoffman-Lane. Our abelianization result holds for smooth quotients, and more generally for quotients which are stratified symplectic spaces in the sense of Sjamaar-Lerman.
