This article is cited in 4 papers

Poisson and Fourier Transforms for Tensor Products

V. F. Molchanov

Tambov State University

Abstract: 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, Poisson and Fourier transforms.

UDC: 517.98

Received: 31.10.2014

DOI: 10.4213/faa3211

 English version: Functional Analysis and Its Applications, 2015, 49:4, 279–288

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