The Wronski map and shifted tableau theory
Abstract
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).
Keywords
Cite
@article{arxiv.1009.0035,
title = {The Wronski map and shifted tableau theory},
author = {Kevin Purbhoo},
journal= {arXiv preprint arXiv:1009.0035},
year = {2010}
}
Comments
11 pages, color figures, identical to v1 but metadata corrected