A third look at weight diagrams
type: Item
instance of: scholarly article
title: A third look at weight diagrams
zbMATH Open document ID: 1016.20029
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2003-04-22T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108535
review text: The author describes how one may compute in the Chevalley groups of type \(E_6\) or \(E_7\) (over a commutative ring) in terms of the weight diagram of a certain fundamental representation. His analysis includes signs of structure constants and signs of the terms in the quadrics that cut out the orbit of a highest weight vector. The story culminates in the `decomposition of unipotents', which is needed to prove the main structure theorems (description of normal subgroups, standard commutator formulae and the like). As is his want, the author provides a lot of background.
Mathematics Subject Classification ID: 20G35
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 1898319
zbMATH Keywords: minimal modules
zbMATH Keywords: Chevalley groups
zbMATH Keywords: Freudenthal transvections
zbMATH Keywords: weight diagrams
zbMATH Keywords: fundamental representations
zbMATH Keywords: highest weight vectors
author: Nikolai Vavilov
reviewed by: Wilberd van der Kallen
MaRDI profile type: Publication
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