Lifting central invariants of quantized Hamiltonian actions

TL;DR

This paper establishes an isomorphism linking the center of a quantized algebra of G-invariant functions on an affine symplectic variety to the Poisson center, advancing understanding of quantized Hamiltonian actions.

Contribution

It introduces a new isomorphism connecting the center of the quantized algebra with the Poisson center of classical invariants, enhancing the theory of quantized Hamiltonian actions.

Findings

Proves an isomorphism between the center of the quantized algebra and the Poisson center.

Extends classical invariants to the setting of Fedosov star-products.

Provides a framework for understanding central invariants in quantized symplectic geometry.

Abstract

Let G be a connected reductive group over an algebraically closed field K of characteristic 0, X an affine symplectic variety equipped with a Hamiltonian action of G. Further, let * be a G-invariant Fedosov star-product on X such that the Hamiltonian action is quantized. We establish an isomorphism between the center of the associative algebra K[X][[h]]^G and the algebra of formal power series with coefficients in the Poisson center of K[X]^G.