Lu, Kang2018-11-302018-11-302018Lu, K. (2018). Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus. Symmetry, Integrability and Geometry: Methods and Applications. https://doi.org/10.3842/SIGMA.2018.046https://hdl.handle.net/1805/17874The 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.enPublisher Policyreal Schubert calculusself-dual spacesBethe ansatzArticle