A quantization of the harmonic analysis on the infinite-dimensional unitary group
type: Item
instance of: scholarly article
title: A quantization of the harmonic analysis on the infinite-dimensional unitary group
zbMATH Open document ID: 1328.43007
author: Vadim Gorin
author: G. I. Olshanskii
published in: Journal of Functional Analysis
publication date: 2015-11-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/1504.06832
review text: The paper under review studies a non-trivial \(q\)-discretization of certain problems related to the harmonic analysis on the infinite dimensional unitary group \(U(\infty)\). The study leads to a new family of determinantal point processes which are connected to pseudo big \(q\)-Jacobi polynomials. These new point processes live on a double \(q\)-lattice and it is shown that their correlation kernels can be expressed through the basic hypergeometric function \({}_2\phi_1\). The main tool introduced in the paper is an extended version of the Gelfand-Tsetlin graph. The \(q\)-boundary of the latter is determined.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 6507487
zbMATH Keywords: noncommutative harmonic analysis
zbMATH Keywords: Gelfand-Tsetlin graph
zbMATH Keywords: determinantal measures
MaRDI profile type: Publication
OpenAlex ID: W2963588972
arXiv ID: 1504.06832
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DOI: 10.1016/J.JFA.2015.06.006
description: scientific article