Moment maps of the spin action and the Cartan-Münzner polynomials of degree four
type: Item
instance of: scholarly article
title: Moment maps of the spin action and the Cartan-Münzner polynomials of degree four
zbMATH Open document ID: 1267.53057
published in: Mathematische Annalen
publication date: 2013-04-03T00:00:00Z
review text: The author expresses all known Cartan-Münzner polynomials of degree four in terms of the square norm of the moment map. He reviews the fundamental concepts and existing results and demonstrates a few theorems, three of them with interesting results. The first theorem is a general one, which expresses the form for the moment map \(\mu\). One of the main results of the article is given by the second theorem which expresses Cartan-Münzner polynomials of degree four in terms of the square norm of the moment map \(\mu \) of a certain group action on \(T \mathbb{R}^{n+1}\), especially of the spin action in the case of OT-FKM type, in both homogeneous and non-homogeneous cases of OT-FKM type in a unified way. Such types are constructed by using the representation of Clifford algebras and in particular, there exists a spin action associated with this algebra. There exist two homogeneous hypersurfaces not of OT-FKM type with \(g = 4\). In these cases, the author expresses \(F(x)\) in the third theorem in terms of the moment map of the isotropy action extended to \(T_{\text{th }}\).
reviewed by: Simona Costache
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53D20
Mathematics Subject Classification ID: 15A66
zbMATH DE Number: 6149476
zbMATH Keywords: Cartan-Münzner polynomials of degree four
zbMATH Keywords: moment maps
zbMATH Keywords: spin action
author: Reiko Miyaoka
MaRDI profile type: Publication
full work available at URL: s00208-012-0819-8
OpenAlex ID: W2105666181
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DOI: 10.1007/S00208-012-0819-8
description: scientific article; zbMATH DE number 6149476