Jeu de taquin and a monodromy problem for Wronskians of polynomials
Abstract
The Wronskian associates to d linearly independent polynomials of degree at most n, a non-zero polynomial of degree at most d(n-d). This can be viewed as giving a flat, finite morphism from the Grassmannian Gr(d,n) to projective space of the same dimension. In this paper, we study the monodromy groupoid of this map. When the roots of the Wronskian are real, we show that the monodromy is combinatorially encoded by Schutzenberger's jeu de taquin; hence we obtain new geometric interpretations and proofs of a number of results from jeu de taquin theory, including the Littlewood-Richardson rule.
Cite
@article{arxiv.0902.1321,
title = {Jeu de taquin and a monodromy problem for Wronskians of polynomials},
author = {Kevin Purbhoo},
journal= {arXiv preprint arXiv:0902.1321},
year = {2009}
}
Comments
37 pages, 3 examples containing figures; detailed example of main theorem added, corrections and clarifications made to some proofs, other minor revisions