Khaled Tounsi | Searcharxiv

arXiv2019

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

We are interested in the study of the space of $n$-ary differential operators denoted by $\mathfrak{D}_{\underlineł,μ}$ where $\underlineł=(ł_{1},...,ł_{n})$ acting on weighted densities from $\frak F_{ł_1}\otimes\frak F_{ł_2}\otimes...\otimes\frak F_{ł_n}$ to $\frak F_μ$ 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 $\mathfrak{D}_{\underlineλ,μ}^k$ to the corresponding space of symbols as well for the explicit expression of the associated quantization map.

math.DG↗

arXiv2014

Symetries of modules of differential operators on $S^{1|1}$

Let $\frak F_ł$ be the space of tensor densities of degree $λ$ on the supercircle $S^{1|1}$. We consider the space $\mathfrak{D}_{λ,μ}^k$ of k-th order linear differential operators from $\frak F_ł$ to $\frak F_μ$ as $\mathfrak{osp}(1|2)$-module and we determine the space $\mathfrak{I}_{λ,μ}^k$ of linear maps on $\mathfrak{D}_{λ,μ}^k$ commuting with the $\mathfrak{osp}(1|2)$-action.

math.RT↗