Lifting central invariants of quantized Hamiltonian actions

Ivan Losev

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

Abstract: Let $G$ be a connected reductive group over an algebraically closed field $\mathbb K$ 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 quantum algebra $\mathbb K[X][[\hbar]]^G$ and the algebra of formal power series with coefficients in the Poisson center of $\mathbb K[X]^G$.

Key words and phrases: reductive groups, Hamiltonian actions, central invariants, quantization.

MSC: 53D20, 53D55, 14R20

Received: March 24, 2008

Language: English

DOI: 10.17323/1609-4514-2009-9-2-359-369

Bibliographic databases:

• 
• 
•