Geodesic
Poisson and Fourier Transforms for Tensor Products
Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 4, pp. 50-60

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For the group $G=\operatorname{SL}(2,\mathbb{R})$, we write out explicitly differential operators intertwining irreducible finite-dimensional representations $T_k$ of $G$ with tensor products $T_{l}\otimes T_{m}$ (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 $G\times G$. The constructions are based on a differential-difference relation for the Poisson kernel.
Keywords: Lie groups and Lie algebras, representations, tensor products
Mots-clés : Poisson and Fourier transforms. 
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     author = {V. F. Molchanov},
     title = {Poisson and {Fourier} {Transforms} for {Tensor} {Products}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {50--60},
     publisher = {mathdoc},
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     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2015_49_4_a3/}
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V. F. Molchanov. Poisson and Fourier Transforms for Tensor Products. Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 4, pp. 50-60. http://geodesic.mathdoc.fr/item/FAA_2015_49_4_a3/