## 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 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.

Original language | English (US) |
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Pages (from-to) | 77-118 |

Number of pages | 42 |

Journal | Advances in Mathematics |

Volume | 190 |

Issue number | 1 |

DOIs | |

State | Published - Jan 15 2005 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Keywords

- Bethe ansatz
- Flag variety
- G
- Gaudin model
- Spin representation
- Wronskian