Abstract
For the group G = SL(2,R), we write out explicitly differential operators intertwining irreducible finite-dimensional representations Tk of G with tensor products Tl ⊗ Tm (we call them Poisson and Fourier transforms); we also describe an analogue of harmonic analysis and write explicit expressions for compositions of these transforms with Lie operators of the overgroup G×G. The constructions are based on a differential-difference relation for the Poisson kernel.
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