Elsevier

Advances in Mathematics

Volume 224, Issue 3, 20 June 2010, Pages 827-862
Advances in Mathematics

Jeu de taquin and a monodromy problem for Wronskians of polynomials

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Abstract

The Wronskian associates to d linearly independent polynomials of degree at most n, a non-zero polynomial of degree at most d(nd). 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 Schützenberger'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.

Keywords

Schubert calculus
Grassmannian
Wronskian
Jeu de taquin
Geometric Littlewood–Richardson rule

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