When is a symplectic quotient an orbifold?

DOI10.1016/j.aim.2015.04.016zbMath1316.53089arXiv1403.3307OpenAlexW2116319358MaRDI QIDQ2346039

Hans-Christian Herbig, Gerald W. Schwarz, Christopher Seaton

Publication date: 29 May 2015

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.3307

zbMATH Keywords

orbifoldssymplectic reduction\(\mathrm{SU}_2\)-representationscircle representations

Mathematics Subject Classification ID

Compact Lie groups of differentiable transformations (57S15) Actions of groups on commutative rings; invariant theory (13A50) Momentum maps; symplectic reduction (53D20) Finite transformation groups (57S17) Linear algebraic groups over the reals, the complexes, the quaternions (20G20)

Related Items (7)

An impossibility theorem for linear symplectic circle quotients ⋮ On \(k\)-polycosymplectic Marsden-Weinstein reductions ⋮ Multigraded Hilbert series of invariants, covariants, and symplectic quotients for some rank 1 Lie groups ⋮ Constructing symplectomorphisms between symplectic torus quotients ⋮ Symplectic quotients have symplectic singularities ⋮ Hilbert series associated to symplectic quotients by SU2 ⋮ Symplectic reduction at zero angular momentum

Uses Software

• Maple
• SL_2_Inv_Ker

Cites Work

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• On orbifold criteria for symplectic toric quotients
• The Koszul complex of a moment map
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• On the existence of star products on quotient spaces of linear Hamiltonian torus actions
• Inequalities defining orbit spaces
• Singular angular momentum mappings
• Polar representations
• A generalization of the Chevalley restriction theorem
• Lifting smooth homotopies of orbit spaces
• Reduction of Hamiltonian systems with symmetry
• Stratified symplectic spaces and reduction
• Geometric and algebraic reduction for singular momentum maps
• Polar Coordinates Induced by Actions of Compact Lie Groups
• Invariant Theory
• EQUIVARIANT SEMI-ALGEBRAIC TRIANGULATIONS OF REAL ALGEBRAIC G-VARIETIES
• Real analytic structures on a symplectic manifold
• Lifting differential operators from orbit spaces
• The Hilbert Series of a Linear Symplectic Circle Quotient

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