Equivariant vector bundles on complete symmetric varieties of minimal rank

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Let X be the wonderful compactification of a complex symmetric space G/H of minimal rank. For a point x∈ G, denote by Z be the closure of BxH/H in X, where B is a Borel subgroup of G. The universal cover of G is denoted by G. Given a G equivariant vector bundle E on X, we prove that E is nef (respectively, ample) if and only if its restriction to Z is nef (respectively, ample). Similarly, E is trivial if and only if its restriction to Z is so.