Symplectic Implosion

The original article can be found at: www.springerlink.comLet 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, Popov, Vinberg, and others. Finally we show that "quantization commutes with implosion"