arXiv subjects
Publications and source records attributed to W. S. Li.
We produce a family of reductions for Schubert intersection problems whose applicability is checked by calculating a linear combination of the dimensions involved. These reductions do not alter the Littlewood-Richardson coefficient, and they lead to an explicit solution of the intersection problem when this coefficient is 1.
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.
We determine the possible eigenvalues of compact selfadjoint operators A,B,C... with the property that A=B+C+... When all these operators are positive, the eigenvalues were known to be subject to certain inequalities which extend Horn's inequalities from the finite-dimensional case when A=B+C. We find the proper extension of the Horn inequalities and show that they, along with their reverse analogues, provide a complete characterization. Our results also allow us to discuss the more general situation where only some of the eigenvalues of the operators are specified. A special case is the requirement that B+C+... be positive of rank at most r.