2014/03/31 by Hans-Christian Herbig, Gerald W. Schwarz, Christopher Seaton · 1 citation
Mathematics · #math.AG #math.RT #math.SG #msc:13A50 #msc:20G20 #msc:53D20 #msc:57S15 #msc:57S17
paper · pdf · doi:10.1016/j.aim.2015.04.016
published as Advances in Mathematics 280 (2015), 208--224 · 14 pages, added extensions of results in version 1 (Theorem 1.3 and Corollary 1.4)
arxiv created 2014/03/31 · arxiv updated 2016/03/18
Let K be a compact Lie group of positive dimension. We show that for most unitary K-modules the corresponding symplectic quotient is not regularly symplectomorphic to a linear symplectic orbifold (the quotient of a unitary module of a finite group). When K is connected, we show that even a symplectomorphism to a linear symplectic orbifold does not exist. Our results yield conditions that preclude the symplectic quotient of a Hamiltonian K-manifold from being locally isomorphic to an orbifold. As an application, we determine which unitary SU2-modules yield symplectic quotients that are ℤ-graded regularly symplectomorphic to a linear symplectic orbifold. We similarly determine which unitary circle representations yield symplectic quotients that admit a regular diffeomorphism to a linear symplectic orbifold.