Projectively equivariant quantization and symbol on supercircle $S^{1|3}$

Bichr, Taher

Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1235-1248.

Résumé

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

Détail

DOI : 10.21136/CMJ.2021.0149-19

Classification : 17B10, 17B66, 53D10
Keywords: differential operator; density; equivariant quantization and orthosymplectic algebra