Tohoku Mathematical Journal
2018
June
SECOND SERIES VOL. 70, NO. 2

Tohoku Math. J.
70 (2018), 319-338

Title MODULES OF BILINEAR DIFFERENTIAL OPERATORS OVER THE ORTHOSYMPLECTIC SUPERALGEBRA $OSP(1/2)$

Author Taher Bichr, Jamel Boujelben and Khaled Tounsi

(Received October 8, 2015, revised April 1, 2016)
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.

Mathematics Subject Classification. Primary 53D10; Secondary 17B66, 17B10.
Key words and phrases. Bilinear differential operators, densities, orthosymplectic algebra, symbol and quantization maps.

To the top of this page

Back to the Contents