Application of multihomogeneous covariants to the essential dimension of finite groups
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
 
ID 97207
Author(s) Lötscher, Roland
Author(s) at UniBasel Lötscher, Roland
Year 2008
Title Application of multihomogeneous covariants to the essential dimension of finite groups
Journal arXiv.org e-Print archive [Elektronische Daten]
Volume 2008, arXiv:0811.3852
Pages / Article-Number 1-34
Keywords essential dimension, covariant dimension, multihomogenization, multihomogeneous covariants, central extension, faithful representations, irreducible components
Abstract We investigate essential dimension of finite groups over arbitrary fields and give a systematic treatment of multihomogenization, introduced by H.Kraft, G.Schwarz and the author. We generalize the central extension theorem of Buhler and Reichstein and use multihomogenization to substitute and generalize the stack-involved part of the theorem of Karpenko and Merkurjev about the essential dimension of p-groups. One part of this paper is devoted to the study of completely reducible faithful representations. Amongst results concerning faithful representations of minimal dimension there is a computation of the minimal number of irreducible components needed for a faithful representation.
Publisher Los Alamos National Laboratory
edoc-URL http://edoc.unibas.ch/dok/A5251835
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