English

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.

Keywords

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

R2 v1 2026-06-21T10:45:55.168Z