Moment maps of the spin action and the Cartan-Münzner polynomials of degree four
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 \(T_{\text{th }}\).
Cartan-Münzner polynomials of degree four
scientific article; zbMATH DE number 6149476
scientific article