A Global version of Grozman’s theorem
Let $$X$$ be a manifold. The classification of all equivariant bilinear maps between tensor density modules over $$X$$ has been investigated by Grozman (Funct Anal Appl 14(2):58–59, 1980), who has provided a full classification for those which are differential operators. Here we investigate the same question without the hypothesis that the maps are differential operators. In our paper, the geometric context is algebraic geometry and the manifold $$X$$ is the circle $$\text{ Spec}\, \mathbb{C }[z,z^{-1}]$$. Our main motivation comes from the fact that such a classification is required to complete the proof of the main result of Iohara and Mathieu (Proc Lond Math Soc, 2012, in press). Indeed it requires to also include the case of deformations of tensor density modules.