Abstract
Let $\frak{F}_\lambda, \lambda\in \mathbb{C}$, be the space of tensor densities of degree $\lambda$ on the supercircle $S^{1|1}$. We consider the superspace $\mathfrak{D}_{\lambda_1,\lambda_2,\mu}$ of bilinear differential operators from $\frak{F}_{\lambda_1}\otimes\frak{F}_{\lambda_2}$ to $\frak{F}_{\mu}$ as a module over the orthosymplectic superalgebra $\mathfrak{osp}(1|2)$. We prove the existence and the uniqueness of a canonical conformally equivariant symbol map from $\mathfrak{D}_{\lambda_1,\lambda_2,\mu}^k$ to the corresponding space of symbols. An explicit expression of the associated quantization map is also given.
Citation
Taher Bichr. Jamel Boujelben. Khaled Tounsi. "Modules of bilinear differential operators over the orthosymplectic superalgebra $\mathfrak{osp}(1|2)$." Tohoku Math. J. (2) 70 (2) 319 - 338, 2018. https://doi.org/10.2748/tmj/1527904824
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