2001/01/18 by Victor Guillemin, Lisa Jeffrey, Reyer Sjamaar · 1 citation
Mathematics · #math.SG #math.AG #msc:53D20 #msc:14L24
published as Transform. Groups 7 (2002), no. 2, 155--184 · 30 pages, LaTeX 2e
arxiv created 2001/01/18 · arxiv updated 2009/11/30
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''.