辛内爆
Symplectic implosion
摘要：
设$K$是紧李群.我们引入辛内爆的过程，它与每一个哈密顿$K$ -流形相关联的分层空间称为内爆截面。它与辛约化有相似之处，但不是由整个群来约化，而是将对称性切割到$K$的极大环面。我们研究的性质的奇点和详细描述的内爆横截面的余切丛的$K$，这原来是相同的仿射品种研究Gelfand，Vinberg，波波夫，和其他人。最后，我们证明了“量子化与内爆互换”。
英文摘要：
Let $K$ be a compact Lie group. We introduce the process of symplectic implosion, which associates to every Hamiltonian $K$-manifold a stratified space called the imploded cross-section. It bears a resemblance to symplectic reduction, but instead of quotienting by the entire group, it cuts the symmetries down to a maximal torus of $K$. We examine the nature of the singularities and describe in detail the imploded cross-section of the cotangent bundle of $K$, which turns out to be identical to an affine variety studied by Gelfand, Vinberg, Popov, and others. Finally we show that ``quantization commutes with implosion''.
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