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arxiv: 1306.0104 · v3 · pith:UVCNEUGWnew · submitted 2013-06-01 · 🧮 math.RT

Symetries of modules of differential operators on S^(1|1)

classification 🧮 math.RT
keywords mathfraklambdafrakspacedifferentiallinearoperatorsaction
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Let $\frak F_{\l}$ be the space of tensor densities of degree $\lambda$ on the supercircle $S^{1|1}$. We consider the space $\mathfrak{D}_{\lambda,\mu}^k$ of k-th order linear differential operators from $\frak F_{\l}$ to $\frak F_{\mu}$ as $\mathfrak{osp}(1|2)$-module and we determine the space $\mathfrak{I}_{\lambda,\mu}^k$ of linear maps on $\mathfrak{D}_{\lambda,\mu}^k$ commuting with the $\mathfrak{osp}(1|2)$-action.

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