This article is cited in 2 papers

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

Kang Lu

Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, 402 North Blackford St, Indianapolis, IN 46202-3216, USA

Abstract: 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.

Keywords: real Schubert calculus; self-dual spaces; Bethe ansatz; Gaudin model.

MSC: 14N99; 17B80; 82B23

Received: November 27, 2017; in final form May 7, 2018; Published online May 14, 2018

Language: English

DOI: 10.3842/SIGMA.2018.046

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