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

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      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

       

      T BICHR1 J BOUJELBEN1 Z SAOUDI1 K TOUNSI1

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

       
  • Proceedings – Mathematical Sciences | News

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