Lower bounds for numbers of real solutions in problems of Schubert calculus
Abstract
We give lower bounds for the numbers of real solutions in problems appearing in Schubert calculus in the Grassmannian Gr(n,d) related to osculating flags. It is known that such solutions are related to Bethe vectors in the Gaudin model associated to gl(n). The Gaudin Hamiltonians are selfadjoint with respect to a nondegenerate indefinite Hermitian form. Our bound comes from the computation of the signature of that form.
 Publication:

arXiv eprints
 Pub Date:
 April 2014
 DOI:
 10.48550/arXiv.1404.7194
 arXiv:
 arXiv:1404.7194
 Bibcode:
 2014arXiv1404.7194M
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematical Physics;
 Mathematics  Algebraic Geometry;
 Mathematics  Combinatorics;
 Mathematics  Representation Theory
 EPrint:
 Latex, 13 pages