On the asymptotics of matrix coefficients of representations of SL(2,R)

DOI10.1016/J.JFA.2024.110476arXiv2306.09038MaRDI QIDQ6440395

V. Losert

Publication date: 15 June 2023

Abstract: We study matrix coefficients of the unitary (and also the completely bounded) representations of SL(2;R) and its universal covering group. We describe the asymptotic distribution of column vectors in terms of Whittaker functions, exhibiting also a relationship to the Fourier transform.

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Analysis on real and complex Lie groups (22E30) Representation theory of linear operators (47A67) Harmonic analysis in one variable (42A99)

Related Items (1)

An infinite-rank Lie algebra associated to \(\mathrm{SL}(2, \mathbb{R})\) and \(\mathrm{SL}(2, \mathbb{R})/U(1)\)

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