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

Symmetry Integrability and Geometry-Methods and Applications

article

Kang Lu¹ 

[1] Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis

关键词: real Schubert calculus;    self-dual spaces;    Bethe ansatz;    Gaudin model;   

DOI  :  10.3842/SIGMA.2018.046

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown