Equivariant embeddings of symmetric spaces

Abstract

For an equivariant embedding of a compact symmetric space X = G/K into a Euclidean G-space the following statements are equivalent:(a) The embedding is extrinsic symmetric.(b) The maximal torus T X of X is rectangular and the representation of G has lowest possible highest weight.(c) The maximal torus T X is embedded as a Clifford torus (an extrinsic product of planar circles).