函子量子化与Guillemin-Sternberg猜想
Functorial quantization and the Guillemin-Sternberg conjecture
摘要：
提出辛流形的几何量子化是函子的箭头部分，其客体部分是泊松流形的形变量子化。Guillemin和Sternberg的“量子化与归约互换”猜想则成为量子化函性的一个特例。事实上，我们的配方产生几乎无限的广义Guillemin-Sternberg猜想，将其扩展，例如，任意李群，甚至李群胚。从技术上讲，这涉及辛约化和温斯坦的对偶对在经典方面，和卡斯帕罗夫的双变K理论C*-代数（KK理论）在量子方面。
英文摘要：
We propose that geometric quantization of symplectic manifolds is the arrow part of a functor, whose object part is deformation quantization of Poisson manifolds. The `quantization commutes with reduction' conjecture of Guillemin and Sternberg then becomes a special case of the functoriality of quantization. In fact, our formulation yields almost unlimited generalizations of the Guillemin--Sternberg conjecture, extending it, for example, to arbitrary Lie groups or even Lie groupoids. Technically, this involves symplectic reduction and Weinstein's dual pairs on the classical side, and Kasparov's bivariant K-theory for C*-algebras (KK-theory) on the quantum side.
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