Intersections of Schubert varieties and eigenvalue inequalities in an arbitrary finite factor

Details Intersections of Schubert varieties and eigenvalue inequalities in an arbitrary finite factor Intersections of Schubert varieties and eigenvalue inequalities in an arbitrary finite factor

2008-05-30

arxiv.org/abs/0805.4817v1

Mathematics

Operator Algebras

41 pages, many figures

Scientific paper

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.

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