The Horn inequalities for submodules

Intersection theory and the Horn inequalities for invariant subspaces

“…It is natural to ask whether a direct connection between these divisibility relations and intersection theory can be made. Indeed, in the context of finitely generated torsion modules over a principal ideal domain, such a connection was made in [10], and it is our purpose to extend that approach to the context of arbitrary C 0 operators. The result is that a sufficient number of these divisibility relations can be obtained from special invariant subspaces M of T .…”

“…The Littlewood-Richardson rule in this context and, indeed, in the case of finitely generated modules over a discrete valuation ring, was first proved in [13] (see also [20] for a different argument.) The basic ideas in this paper originated in the study of singular numbers for products of operators [8] and in the study of torsion modules over principal ideal domains [10]. The techniques we use are necessarily different, and they may obscure to some extent the essential simplicity of the arguments.…”