Browsing by Subject "real Schubert calculus"

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    Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus
    (National Academy of Science of Ukraine, 2018) Lu, Kang; Mathematical Sciences, School of Science
    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.