Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus

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 number of real self-dual spaces in intersections of Schubert varieties related to osculating flags in the Grassmannian. Th...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2018
Main Author: Lu, K.
Format: Article
Language:English
Published: Інститут математики НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209526
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus / K. Lu // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 20 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary: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 number 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.
ISSN:1815-0659