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- Title
The Wronski Map and Shifted Tableau Theory.
- Authors
Purbhoo, Kevin
- 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)⊂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).
- Subjects
WRONSKIAN determinant; DIFFERENTIAL equations; GRASSMANN manifolds; MANIFOLDS (Mathematics); DIFFERENTIAL topology; POLYNOMIALS
- Publication
IMRN: International Mathematics Research Notices, 2011, Vol 2011, Issue 24, p5706
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnq295