Symplectic reduction at zero angular momentum (Q254838)

The authors of the paper under review examine geometric and algebraic properties of symplectic quotients corresponding to \(k\) particles moving in \(\mathbb R^n\) with zero angular momentum. They model the phase space of configurations of the \(k\) particles and describe the symplectic quotients of zero angular momentum by \(\mathrm{O}_n\) and \(\mathrm{SO}_n\). They construct maps between the two quotients based on polynomial invariant theory. They show that the symplectic quotient by \(\mathrm{O}_n\) is symplectomorphic to a linear symplectic orbifold if and only if \(k=1\) or \(n=1\). They also show that when \(n \leq k\) the zero fibre of the moment map has rational singularities. At the end they use computational methods to describe some algebras related to symplectic quotients.