Self-self-dual spaces of polynomials

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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 G_2-populations related to the Bethe Ansatz of the Gaudin model of type G_2 and prove that a G_2-population is isomorphic to the G_2 flag variety.
Latex, 38 pages

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Quantum Algebra, Algebraic Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/68309

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0308128
 http://arxiv.org/abs/math/0308128

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arXiv