Self-self-dual spaces of polynomials

2003/08/13 by Lev Borisov, E. Mukhin, Borisov, Lev +2 · 2 citations
Computer Science · Mathematics · #Advanced Banach Space Theory #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Optimization and Variational Analysis #Quantum Algebra (math.QA) #math.AG #math.QA

paper · pdf · doi:10.48550/arxiv.math/0308128

Latex, 38 pages

arxiv created 2003/08/13 · openalex publication_date 2003/08/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A space of polynomials V of dimension 7 is called self-dual if the divided Wronskian of any 6-subspace is in V. A self-dual space V has a natural inner product. The divided Wronskian of any isotropic 3-subspace of V is a square of a polynomial. We call V self-self-dual if the square root of the divided Wronskian of any isotropic 3-subspace is again in V. We show that the self-self-dual spaces have a natural non-degenerate skew-symmetric 3-form defined in terms of Wronskians. We show that the self-self-dual spaces correspond to G₂-populations related to the Bethe Ansatz of the Gaudin model of type G₂ and prove that a G₂-population is isomorphic to the G₂ flag variety.

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