Symmetries of Modules of Differential Operators

Abstract

Let be the space of tensor densities of degree (or weight) λ on the circle S1. The space of k-th order linear differential operators from to is a natural module over Diff(S1), the diffeomorphism group of S 1. We determine the algebra of symmetries of the modules , i.e., the linear maps on commuting with the Diff(S 1)-action. We also solve the same problem in the case of straight line ℝ (instead of S 1) and compare the results.