Conformally equivariant quantization and symbol maps associated with $n$-ary differential operators on weighted densities

Abstract

We are interested in the study of the space of $n$-ary differential operators denoted by ${\mathfrak{D}}_{\underline{ł},\mu }$ where $\underline{ł}=({ł}_1,...,{ł}_n)$ acting on weighted densities from ${\mathfrak{F}}_{{ł}_1}\otimes {\mathfrak{F}}_{{ł}_2}\otimes ...\otimes {\mathfrak{F}}_{{ł}_n}$ to ${\mathfrak{F}}_{\mu }$ as a module over the orthosymplectic superalgebra $\mathfrak{osp}(1|2)$. As a consequence, we prove the existence and the uniqueness of a canonical conformally equivariant symbol map from ${\mathfrak{D}}_{\underline{\lambda },\mu }^k$ to the corresponding space of symbols as well for the explicit expression of the associated quantization map.

14 pages. arXiv admin note: text overlap with arXiv:1302.3727 by other authors

References in corpus (2)

• Natural and Projectively Invariant Quantizations on Supermanifolds
• The space of m-ary differential operators as a module over the Lie algebra of vector fields