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2018 Modules of bilinear differential operators over the orthosymplectic superalgebra $\mathfrak{osp}(1|2)$
Taher Bichr, Jamel Boujelben, Khaled Tounsi
Tohoku Math. J. (2) 70(2): 319-338 (2018). DOI: 10.2748/tmj/1527904824

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.

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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

Information

Published: 2018
First available in Project Euclid: 2 June 2018

zbMATH: 06929337
MathSciNet: MR3810243
Digital Object Identifier: 10.2748/tmj/1527904824

Subjects:
Primary: 53D10
Secondary: 17B10, 17B66

Rights: Copyright © 2018 Tohoku University

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Vol.70 • No. 2 • 2018
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