Intersections of Schubert varieties and eigenvalue inequalities in an arbitrary finite factor
Operator Algebras
2019-02-27 v1 Combinatorics
Abstract
It is known that the eigenvalues of selfadjoint elements a,b,c with a+b+c=0 in the factor R^omega (ultrapower of the hyperfinite II1 factor) are characterized by a system of inequalities analogous to the classical Horn inequalities of linear algebra. We prove that these inequalities are in fact true for elements of an arbitrary finite factor. A matricial (`complete') form of this result is equivalent to an embedding question formulated by Connes.
Cite
@article{arxiv.0805.4817,
title = {Intersections of Schubert varieties and eigenvalue inequalities in an arbitrary finite factor},
author = {H. Bercovici and B. Collins and K. Dykema and W. S. Li and D. Timotin},
journal= {arXiv preprint arXiv:0805.4817},
year = {2019}
}
Comments
41 pages, many figures