  The Wronski map is a finite, PGL_2(C)-equivariant morphism from the
Grassmannian Gr(d,n) to a projective space (the projectivization of a vector
space of polynomials). We consider the following problem. If C_r < PGL_2(C) is
a cyclic subgroup of order r, how may C_r-fixed points are in the in a fibre of
the Wronski map over a C_r-fixed point in the base?
  In this paper, we compute a general answer in terms of r-ribbon tableaux.
When r=2, this computation gives the number of real points in the fibre of the
Wronski map over a real polynomial with purely imaginary roots. More generally,
we can compute the number of real points in certain intersections of Schubert
varieties.
  When r divides d(n-d) our main result says that the generic number of
C_r-fixed points in the fibre is the number of standard r-ribbon tableaux
rectangular shape (n-d)^d. Computing by a different method, we show that the
answer in this case is also given by the number of of standard Young tableaux
of shape (n-d)^d that are invariant under N/r iterations of jeu de taquin
promotion. Together, these two results give a new proof of Rhoades' cyclic
sieving theorem for promotion on rectangular tableaux.
  We prove analogous results for dihedral group actions.
