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Lower bounds for numbers of real solutions in problems of Schubert calculus

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Acta Mathematica

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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Authors and Affiliations

  1. Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN, 46202, U.S.A.

    Evgeny Mukhin & Vitaly Tarasov

  2. St. Petersburg Branch of Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191023, Russia

    Vitaly Tarasov

Authors
  1. Evgeny Mukhin
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  2. Vitaly Tarasov
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Correspondence to Evgeny Mukhin.

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Mukhin, E., Tarasov, V. Lower bounds for numbers of real solutions in problems of Schubert calculus. Acta Math 217, 177–193 (2016). https://doi.org/10.1007/s11511-016-0143-3

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  • DOI: https://doi.org/10.1007/s11511-016-0143-3

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