Deformation of $\mathfrak{osp}(2|2)$-Modules of Symbols

TL;DR

This paper classifies how the module structure of symbols associated with differential operators on weighted densities deforms under the action of the superalgebra rak{osp}(2|2), providing a detailed understanding of their algebraic properties.

Contribution

It offers the first classification of deformations of rak{osp}(2|2)-modules on symbol spaces of differential operators on weighted densities.

Findings

Complete classification of deformations of rak{osp}(2|2)-modules

Identification of conditions for module deformations

Explicit description of deformed module structures

Abstract

We classify deformations of $\mathfrak{osp}(2|2)-$module structure on the spaces of symbols $\mathfrak{S}_d^2$ of differential operators acting on the space of weighted densities $\mathfrak{F}_{\lambda}^{2}$.