Eisenstein series on weakly spherical homogeneous spaces of \(GL(n)\)
type: Item
instance of: scholarly article
title: Eisenstein series on weakly spherical homogeneous spaces of \(GL(n)\)
zbMATH Open document ID: 0944.11017
author: Fumihiro Sato
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2000-09-20T00:00:00Z
review text: Let \(G\) be a connection reductive algebraic group and let \(P\) be a proper parabolic subgroup. A homogeneous space \(X=G/H\) is called \(P\)-spherical if there exists a Zariski-open \(P\)-orbit in \(X\). It is also called weakly spherical. The purpose of this paper is to construct generalized Eisenstein series attached to the weakly spherical homogeneous space when \(G\) is a product of several general linear groups and \(P\) is its (not necessarily maximal) parabolic subgroup. The author of this paper constructed generalized Eisenstein series as complex multivariate functions and proved that they are meromorphic with respect to the complex numbers under suitable conditions on \(P\) and \(H\). Then he proves that Eisenstein series satisfy functional equations and give their explicit forms.
reviewed by: Masakazu Muro
Mathematics Subject Classification ID: 11F55
zbMATH DE Number: 1185532
zbMATH Keywords: generalized Eisenstein series
zbMATH Keywords: weakly spherical homogeneous space
zbMATH Keywords: functional equations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225014
OpenAlex ID: W2030207652
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DOI: 10.2748/TMJ/1178225014
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description: scientific article; zbMATH DE number 1185532