  The lower dimensional Busemann-Petty problem asks, whether n-dimensional
centrally symmetric convex bodies with smaller i-dimensional central sections
necessarily have smaller volumes. The paper contains a complete solution to the
problem when the body with smaller sections is invariant under rotations,
preserving mutually orthogonal coordinate subspaces of fixed dimension. The
argument relies on the notion of canonical angles between subspaces, spherical
Radon transforms, properties of intersection bodies, and the generalized cosine
transforms.
