Scale functions on linear groups over local skew fields
type: Item
instance of: scholarly article
title: Scale functions on linear groups over local skew fields
zbMATH Open document ID: 0910.20028
author: Helge Glöckner
published in: Journal of Algebra
publication date: 1999-03-22T00:00:00Z
review text: Certain questions in the theory of probability measures led G. Willis to the definition of the ``scale function'' on a totally disconnected locally compact group. This function with values in the natural numbers gives some insight into the structure of the group. In the present paper the scale function is computed on diagonal matrices in the general or special linear groups or in the group of triangular matrices over a local skew field. It is computed completely on \(\text{GL}(2,K)\) and \(\text{SL}(2,K)\) when \(K\) is a commutative local field. All computed values of the scale function are integral powers of \(q\), the number of elements of the residue field, so that it is possible to recover \(q\) from (partial) knowledge of the scale function.
Mathematics Subject Classification ID: 20G25
zbMATH DE Number: 1214131
zbMATH Keywords: scale functions
zbMATH Keywords: locally compact groups
zbMATH Keywords: special linear groups
zbMATH Keywords: groups of triangular matrices
zbMATH Keywords: general linear groups
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
full work available at URL: jabr.1997.7409
OpenAlex ID: W2034488828
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DOI: 10.1006/JABR.1997.7409
description: scientific article; zbMATH DE number 1214131