The rationality of the fields of invariants of reducible representations of the group \(SL_ 2\)
type: Item
instance of: scholarly article
title: The rationality of the fields of invariants of reducible representations of the group \(SL_ 2\)
zbMATH Open document ID: 0582.20032
published in: Moscow University Mathematics Bulletin
publication date: 1984-01-01T00:00:00Z
review text: Let V(d) be the space of homogeneous polynomials of degree d in two variables, and \(V=V(d(1))\times...\times V(d(k))\) for some d(1),...,d(k). On V there exists a natural action of the group \(G=SL_ 2\times ({\mathbb{C}}^*)^ k\). The main theorem of the note states that the field of invariants \({\mathbb{C}}[V]^ G\) is rational for all k with the only possible exception \(k=1\), d(1) even.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 15A72
zbMATH DE Number: 3931264
zbMATH Keywords: homogeneous polynomials
zbMATH Keywords: action
zbMATH Keywords: field of invariants
author: Pavel I. Katsylo
reviewed by: Sergei Gelfand
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3931264