The index of equidimensional flag manifolds

Abstract In this paper, we consider the flag manifold of orthogonal subspaces of equal dimension that carries an action of the cyclic group of order . We provide a complete calculation of the associated Fadell–Husseini index. This may be thought of as an odd primary version of the computations of Baralić, Blagojevic, Karasev, and Vucic, for the Grassmann manifold . These results have geometric consequences for ‐fold orthogonal shadows of a convex body.