Shapiro Conjecture : Part II: Flag Manifolds and Beyond

Part II: Flag Manifolds and Beyond

The original Shapiro Conjecture was for the classical flag manifold, but it makes sense for any flag manifold G/P, including the Grassmannian.

Unfortunately, the Shapiro Conjecture fails in the simplest problem on a flag manifold that is not a Grassmannian, but in a very interesting way.

The conjecture can be repaired, and there is considerable evidence supporting the new conjecture, including asymptotic results, proofs of the new conjecture involving rational functions, and a very appealing generalization.