## Advanced Studies in Pure Mathematics

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

Reiko Miyaoka

#### Abstract

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.

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