Symplectic Implosion
Symplectic Implosion
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辛内爆
DOI：
10.1007/s00031-002-0009-y
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发表时间：
2001
影响因子：
0.7
通讯作者：
Reyer Sjamaar
中科院分区：
文献类型：
--
作者：
V. Guillemin;L. Jeffrey;Reyer Sjamaar
． 设K是紧李群。我们引入了辛内爆过程，它将每一个哈密顿K流形与一个称为内爆截面的分层空间联系起来。它与辛还原有相似之处，但不是对整个群进行引用，而是将对称性减少到K的最大环面。我们研究了奇点的性质，并详细描述了K的协切束的内爆截面，结果证明它与Gelfand， Vinberg， Popov等人研究的仿射变体相同。最后我们证明了“量子化与内爆交换”。
. 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”.