On a system of basis invariants of the group \(E_ 7\)
type: Item
instance of: scholarly article
title: On a system of basis invariants of the group \(E_ 7\)
zbMATH Open document ID: 0869.20033
DOI: 10.1007/BF02362675
author: L. V. Glushkova
published in: Journal of Mathematical Sciences (New York)
publication date: 1997-06-26T00:00:00Z
review text: Suppose a rectangular Cartesian coordinate system \(Ox_i\), \(i=\overline{1,7}\), is defined in the real Euclidean space \(E_7\). The hyperplanes of symmetry of the Gosset polyhedron \(3_{21}\) that are invariant relative to the group \(E_7\) can be defined by the normalized equations \(\eta_s=0\), \(s=\overline{1,63}\). The basis invariants of the group \(E_7\) have degrees \(n_i=2,6,8,10,12,14,18\). \textit{V. F. Ignatenko} [Ukr. Geom. Sb. 23, 50-56 (1980; Zbl 0475.14007)] has proved the following result. Theorem. The polynomials \(P_{2s}=\sum^{63}_{s=1}\eta^{n_i}_s\), \(i=\overline{1,7}\), form a system of basis invariants of the group \(E_7\). In this paper we give a new proof of this theorem (using a computer).
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 51N35
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 14L35
zbMATH DE Number: 1026968
zbMATH Keywords: hyperplanes of symmetry
zbMATH Keywords: Gosset polyhedron
zbMATH Keywords: basis invariants
MaRDI profile type: Publication
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cites work: The classes and representations of the groups of 27 lines and 28 bitangents
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description: scientific article; zbMATH DE number 1026968