Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus

Kang Lu

Symmetry, integrability and geometry: methods and applications, Tome 14 (2018)

Résumé

The self-dual spaces of polynomials are related to Bethe vectors in the Gaudin model associated to the Lie algebras of types B and C. In this paper, we give lower bounds for the numbers of real self-dual spaces in intersections of Schubert varieties related to osculating flags in the Grassmannian. The higher Gaudin Hamiltonians are self-adjoint with respect to a nondegenerate indefinite Hermitian form. Our bound comes from the computation of the signature of this form.

Détail

Keywords: real Schubert calculus; self-dual spaces; Bethe ansatz; Gaudin model.

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