Weyl invariant polynomial and deformation quantization on Kahler manifolds

Abstract

Given a polynomial P of partial derivatives of the Kahler metric, expressed as a linear combination of directed multigraphs, we prove a simple criterion in terms of the coefficients for $P$ to be an invariant polynomial, i.e. invariant under the transformation of coordinates. As applications, we prove an explicit composition formula for covariant differential operators under a canonical basis, also known as invariant differential operators in the case of bounded symmetric domains. We also prove a general explicit formula of star products on Kahler manifolds.

17 pages

References in corpus (6)

• A closed formula for the asymptotic expansion of the Bergman kernel
• An explicit formula for the Berezin star product
• A Universal Formula for Deformation Quantization on Kähler Manifolds
• On a formula of Gammelgaard for Berezin-Toeplitz quantization
• On Gammelgaard's formula for a star product with separation of variables
• Deformation quantization with separation of variables of an endomorphism bundle

Cited by in corpus (1)

• Heat kernel coefficients on Kahler manifolds