Full reducibility and invariants for \(\text{SL}_2(\mathbb{C})\)
type: Item
instance of: scholarly article
title: Full reducibility and invariants for \(\text{SL}_2(\mathbb{C})\)
zbMATH Open document ID: 0985.20028
published in: L'Enseignement Mathématique. 2e Série
publication date: 2001-01-30T00:00:00Z
review text: A representation \(V\) of a group \(G\) is called fully reducible if it is a direct sum of irreducible representations. The paper is focused on the case when \(G=\text{SL}_2(\mathbb{C})\) (complex \(2\times 2\) matrices with determinant 1) and \(V\) is any finite-dimensional complex holomorphic representation. The full reducibility in this case is a fact with an interesting history. Details of different proofs are given. More general situations and connections with invariant theory and other problems are also discussed.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 20-03
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 20G20
zbMATH DE Number: 1558721
zbMATH Keywords: full reducibility
zbMATH Keywords: invariants
zbMATH Keywords: representations
zbMATH Keywords: groups of complex matrices
zbMATH Keywords: historical survey
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
author: Armand Borel
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description: scientific article; zbMATH DE number 1558721