Modules of third-order differential operators on a conformally flat manifold

✍ Scribed by S.E. Loubon Djounga

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 86 KB
• Volume: 37
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(00)00047-4

✦ Synopsis

Let M be a smooth manifold endowed with a flat conformal structure and F λ (M) the space of densities of degree λ on M. We study the space D 3 λ,µ (M) of third-order differential operators from F λ (M) to F µ (M) as a module over the conformal Lie algebra o(p + 1, q + 1). We prove that D 3 λ,µ (M) is isomorphic to the corresponding module of third-order polynomials on T * (M) for almost all values of δ = µ -λ, except for eight resonant values. The isomorphism is unique and will be given explicitly, yielding a conformally equivariant quantization. We also study the modules in the case of resonance.