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Keywords:
differential operator; density; equivariant quantization and orthosymplectic algebra
differential operator; density; equivariant quantization and orthosymplectic algebra
Summary:
Let $\mathcal {D}_{\lambda ,\mu } $ be the space of linear differential operators on weighted densities from $\mathcal {F}_{\lambda }$ to $\mathcal {F}_{\mu }$ as module over the orthosymplectic Lie superalgebra $\mathfrak {osp}(3|2)$, where $\mathcal {F}_{\lambda } $, $ł\in \nobreak \mathbb {C}$ is the space of tensor densities of degree $\lambda $ on the supercircle $S^{1|3}$. We prove the existence and uniqueness of projectively equivariant quantization map from the space of symbols to the space of differential operators. An explicite expression of this map is also given.\looseness -1
References:
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