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.