Moment map of the spin action and the Cartan-Münzner Polynomials

摘要

We describe the Cartan-Münzner polynomials of degree four on an N-dimensional Euclidean space by using the square norm of the moment map of certain group actions. In the case of OT-FKM type, the action is a spin action which is not necessarily transitive on isoprametric hypersurfaces.