Gordan-Rankin-Cohen operators on the spaces of weighted densities in superdimension $1\vert 1$

TL;DR

This paper classifies Gordan-Rankin-Cohen differential operators on weighted densities in superdimension 1|1, extending previous results to supermanifolds and offering open problems.

Contribution

It provides a classification of Gordan-Rankin-Cohen operators on weighted densities in superdimension 1|1, generalizing prior work to supermanifolds.

Findings

Classification of operators on supermanifolds in superdimension 1|1

Extension of previous results to superstrings

Open problems proposed for further research

Abstract

The modular forms and weighted densities over the 1-dimensional manifold $M$ are transformed ``alike" under the group of linear fractional changes of coordinates, so the classifications of differential operators between spaces of (A) modular forms and (B) weighted densities are sometimes identified, although they are different. Here, we solve problem B for superstrings in superdimension $(1\vert 1)$ -- superizations of the result of arXiv:2404.18222. Open problems are offered.