Symplectic Implosion
By V. Guillemin, L. Jeffrey, Reyer Sjamaar. 2001
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. 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”.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/7b5cb6868d88f8625f91ee4ce16021e75f5b068a
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Proof of the Knop conjecture (2006, result): “of t+ containing iimψL. Put Ye := Φ−1(t0 + ×z). Replacing Kwith a covering we may assume that Kis the direct product of a torus and a simply connected semisimple group. It follows now from results of [GJS] (see especially Theorem 4.9, Theorem 6.11, and the proof of Theorem 6.17) that there is a Te K”