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arXiv · math-ph/0610059

Differential operators on supercircle: conformally equivariant quantization and symbol calculus

Hichem Gargoubi·Najla Mellouli·Valentin Ovsienko
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Abstract

We consider the supercircle $S^{1|1}$ equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on $S^{1|1}$ as the Lie superalgebra of contact vector fields; it contains the Möbius superalgebra $osp(1|2)$. We study the space of linear differential operators on weighted densities as a module over $osp(1|2)$. We introduce the canonical isomorphism between this space and the corresponding space of symbols and find interesting resonant cases where such an isomorphism does not exist.

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Hichem Gargoubi, Najla Mellouli, Valentin Ovsienko. 2006-10-30. Differential operators on supercircle: conformally equivariant quantization and symbol calculus. https://doi.org/10.1007/s11005-006-0129-8

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