A formula for the number of semi-simple conjugacy classes in the arithmetic subgroups
type: Item
instance of: scholarly article
title: A formula for the number of semi-simple conjugacy classes in the arithmetic subgroups
zbMATH Open document ID: 0577.10023
author: Ki-ichiro Hashimoto
published in: Proceedings of the Japan Academy. Series A
publication date: 1985-01-01T00:00:00Z
review text: It would be appropriate to quote some sentences from the paper with slight modifications. - The purpose of this note is to present a general formula for the number of conjugacy classes in the arithmetic subgroups of a reductive algebraic group G defined over an algebraic number field k, of those elements which are contained in a semi-simple conjugacy class of \(G_ k\). With the knowledge of the parametrization of \(G_ k\)- conjugacy classes developed in the relevant papers, the formula obtained in this paper gives us an effective procedure to count explicitly the number of semi-simple conjugacy classes with given characteristic polynomials in a wide class of arithmetic subgroups of the classical groups.
reviewed by: Michio Ozeki
Mathematics Subject Classification ID: 11F06
Mathematics Subject Classification ID: 11F70
zbMATH DE Number: 3922759
zbMATH Keywords: number of conjugacy classes
zbMATH Keywords: arithmetic subgroups
zbMATH Keywords: reductive algebraic group
zbMATH Keywords: number of semi-simple conjugacy classes
MaRDI profile type: Publication
full work available at URL: pjaa.61.48
OpenAlex ID: W2071271514
cites work: The conjugacy classes in the unitary, symplectic and orthogonal groups over an algebraic number field
cites work: Q3870964
cites work: On certain elliptic conjugacy classes of the Siegel modular group
cites work: On the connective K-homology groups of the classifying spaces \(B{\mathbb{Z}}/p^ r\)
cites work: Q3898575
cites work: Involutive modular transformations on the Siegel upper half plane and an application to representations of quadratic forms
cites work: On the number of regular elliptic conjugacy classes in the Siegel modular group of degree 2n
cites work: On isometries of inner product spaces
cites work: On the conjugacy classes in the unitary, symplectic and orthogonal groups
cites work: Q5662587
DOI: 10.3792/PJAA.61.48
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description: scientific article; zbMATH DE number 3922759