Lower bounds for numbers of real solutions in problems of Schubert calculus |
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| Authors: | Evgeny Mukhin Vitaly Tarasov |
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| Institution: | 1.Department of Mathematical Sciences,Indiana University – Purdue University Indianapolis,Indianapolis,U.S.A.;2.St. Petersburg Branch of Steklov Mathematical Institute,St. Petersburg,Russia |
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| Abstract: | We give lower bounds for the numbers of real solutions in problems appearing in Schubert calculus in the Grassmannian \({\mathop{\rm Gr}(n,d)}\) related to osculating flags. It is known that such solutions are related to Bethe vectors in the Gaudin model associated to \({\mathop{\rm gl}_n}\). 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. |
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