• Modules of $n$-ary differential operators over the orthosymplectic superalgebra $\mathscr{osp(1|2)}$

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/131/0011

• # Keywords

$n$-Ary differential operators; densities; orthosymplectic algebra; symbol; quantization maps.

• # Abstract

We are interested in the study of the space of $n$-ary differential operators denoted by $\mathscr{D}_{\underline{\lambda},\mu}$ where $\underline{\lambda}=(\lambda_1, \ldots ,\lambda_n)$ is acting on weighted densities from $\mathsci{F}\lambda_1\otimes\mathsci{F}\lambda_2\otimes\cdots\otimes\mathsci{F}\lambda_n$ to $\mathsci{F}\mu$ as a module over the orthosymplectic superalgebra $\mathscr{osp(1|2)}$. As a consequence, we prove the existence and the uniqueness of a canonical conformally equivariant symbol map from $\mathscr{D}^k_{\lambda , \mu}$ to the corresponding space of symbols as well for the explicit expression of the associated quantization map.

• # Author Affiliations

1. Département de Mathematiques, Faculte des sciences de Sfax, BP 1171, 3000 Sfax, Tunisie

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019