On the existence of star products on quotient spaces of linear Hamiltonian torus actions

Abstract

We discuss BFV deformation quantization of singular symplectic quotient spaces in the special case of linear Hamiltonian torus actions. In particular, we show that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic. We rephrase the nonpositivity condition of Arms, Gotay and Jennings for linear Hamiltonian torus actions. It follows that reduced spaces of such actions admit continuous star products.

9 pages, 4 figures, uses psfrag

References in corpus (2)

• Lectures on 0/1-polytopes
• Variations on Homological Reduction

Cited by in corpus (10)

• The Hilbert series of a linear symplectic circle quotient
• Symplectic quotients have symplectic singularities
• When is a symplectic quotient an orbifold?
• On Orbifold Criteria for Symplectic Toric Quotients
• On compositions with $x^2/(1-x)$
• An impossibility theorem for linear symplectic circle quotients
• Hilbert series of symplectic quotients by the 2-torus
• Constructing symplectomorphisms between symplectic torus quotients
• Symplectic quotients and representability: the circle action case
• Multigraded Hilbert series of invariants, covariants, and symplectic quotients for some rank $1$ Lie groups