  The Mukhin-Tarasov-Varchenko Theorem, conjectured by B. and M. Shapiro, has a
number of interesting consequences. Among them is a well-behaved correspondence
between certain points on a Grassmannian - those sent by the Wronski map to
polynomials with only real roots - and (dual equivalence classes of) Young
tableaux.
  In this paper, we restrict this correspondence to the orthogonal Grassmannian
OG(n,2n+1) inside Gr(n,2n+1). We prove that a point lies on OG(n,2n+1) if and
only if the corresponding tableau has a certain type of symmetry. From this we
recover much of the theory of shifted tableaux for Schubert calculus on
OG(n,2n+1), including a new, geometric proof of the Littlewood-Richardson rule
for OG(n,2n+1).
