2010/08/31 by Purbhoo, Kevin
#14N15 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1009.0035
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).