Vladimir Molchanov

Poisson and Fourier transforms for tensor products

We write explicitly operators intertwining finite-dimensional representations of the group $G={\rm SL} (2, {\Bbb R})$ with their tensor products. We call these operators {\it Poisson} and {\it Fourier transforms} respectively, they are conjugate to each other. We also write explicitly an interaction of these transforms with Lie operators of the overgroup $G\times G$. All these operators (transforms etc.) turn out to be {\it differential} operators.