Browsing by Subject "real solutions"

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    Lower bounds for numbers of real solutions in problems of Schubert calculus
    (Springer, 2016-09) Mukhin, Evgeny; Tarasov, Vitaly; Mathematical Sciences, School of Science
    We give lower bounds for the numbers of real solutions in problems appearing in Schubert calculus in the Grassmannian Gr(n,d)Gr⁡(n,d) related to osculating flags. It is known that such solutions are related to Bethe vectors in the Gaudin model associated to glngln. The Gaudin Hamiltonians are self-adjoint with respect to a non-degenerate indefinite Hermitian form. Our bound comes from the computation of the signature of that form.