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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 046, 15 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.046 (Mi sigma1345) 		 
This article is cited in 2 scientific papers (total 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
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DOI: https://doi.org/10.3842/SIGMA.2018.046
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.
Funding agency Grant number
Zhejiang Provincial Natural Science Foundation of China LY14A010018
This work was partially supported by Zhejiang Province Science Foundation, grant No. LY14A010018.
Received: November 27, 2017; in final form May 7, 2018; Published online May 14, 2018
Bibliographic databases:
Document Type: Article
MSC: 14N99; 17B80; 82B23
Language: English
Citation: Kang Lu, “Lower Bounds for Numbers of Real Self-Dual Spaces in Problems of Schubert Calculus”, SIGMA, 14 (2018), 046, 15 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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