Lower bounds for numbers of real solutions in problems of Schubert calculus
Quantum Algebra
2014-04-30 v1 Mathematical Physics
Algebraic Geometry
Combinatorics
math.MP
Representation Theory
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.
Keywords
Cite
@article{arxiv.1404.7194,
title = {Lower bounds for numbers of real solutions in problems of Schubert calculus},
author = {E. Mukhin and V. Tarasov},
journal= {arXiv preprint arXiv:1404.7194},
year = {2014}
}
Comments
Latex, 13 pages