Endomorphisms of real Grassmannians that commute with Steenrod squares.

For k ∈ {2, 3} we classify endomorphisms of H∗ (Gk,n; Z2) that commute with Steenrod squares (here, Gk,n denotes the Grassmann manifold of k-dimensional subspaces in Rn+k ). Additionally, for all positive integers k and n we classify endomorphisms of H∗ (Gk,n; Z2) that commute with Steenrod squares and such that the image of each class is a polynomial in the (nonzero) class of H1 (Gk,n; Z2) [ABSTRACT FROM AUTHOR]