Abstract :
[en] Let F_lambda(S^1) be the space of tensor densities of degree (or weight) lambda on the circle S^1. The space D_lambda,mu(k)(S^1) of k-th order linear differential operators from F_lambda(S^1) to F_mu(S^1) is a natural module over Diff(S^1), the diffeomorphism group of S^1. We determine the algebra of symmetries of the modules D_lambda,mu(k)(S^1), i.e., the linear maps on D_lambda,mu(k)(S^1) 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.
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