An impossibility theorem for linear symplectic circle quotients

Abstract

We prove that when $d>2$, a $d$-dimensional symplectic quotient at the zero level of a unitary circle representation $V$ such that $V^{\Sp^1}=\{0\}$ cannot be $\mathbb{Z}$-graded regularly symplectomorphic to the quotient of a unitary representations of a finite group.

26 pages

References in corpus (3)

• The Hilbert series of a linear symplectic circle quotient
• When is a symplectic quotient an orbifold?
• On Orbifold Criteria for Symplectic Toric Quotients

Cited by in corpus (7)

• Symplectic quotients have symplectic singularities
• When is a symplectic quotient an orbifold?
• Symplectic reduction at zero angular momentum
• Hilbert series associated to symplectic quotients by ${\mathrm{SU}}_2$
• Hilbert series of symplectic quotients by the 2-torus
• Constructing symplectomorphisms between symplectic torus quotients
• Multigraded Hilbert series of invariants, covariants, and symplectic quotients for some rank $1$ Lie groups