Probability measures on dual objects to compact symmetric spaces, and hypergeometric identities.
type: Item
instance of: scholarly article
title: Probability measures on dual objects to compact symmetric spaces, and hypergeometric identities.
zbMATH Open document ID: 1075.43009
publication date: 2005-02-25T00:00:00Z
review text: The author presents several proofs of some combinatorial identities which may be regarded as multidimensional analogs of Dougall's formula for bilateral hypergeometric series. The main proof uses representations of series of classical compact symmetric spaces which finally leads to these identities for discrete parameters. The general case is the obtained via analytic continuation by Carlson's theorem. This approach also shows that these identities are connected with the construction of concrete spherical functions on inductive limits of symmetric spaces. The author also observes that his identities are special cases of older formulas of R. A. Gustafson. Moreover, connections to Selberg-type integrals are discussed.
reviewed by: Michael Voit
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 33C99
Mathematics Subject Classification ID: 60B05
zbMATH DE Number: 2138546
zbMATH Keywords: multidimensional version of Dougall's formula
zbMATH Keywords: spherical functions
zbMATH Keywords: series of classical symmetric space
zbMATH Keywords: formula of Gustafson
author: G. I. Olshanskii
MaRDI profile type: Publication
full work available at URL: b:faia.0000015579.81046.cb
OpenAlex ID: W2083253682
DOI: 10.1023/B:FAIA.0000015579.81046.CB
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 2138546