On a conjectured formula for quiver varieties
Abstract
Description
In our joint paper with W. Fulton (math.AG/9804041) we prove a formula for the cohomology class of a quiver variety. This formula involves a new class of generalized Littlewood-Richardson coefficients, all of which surprisingly seem to be non-negative. We conjecture that each of these coefficients count the number of sequences of semistandard Young tableaux which satisfy certain conditions.
In this paper I give a proof of this conjecture in the special case where the quiver variety can be described by at most four vector bundles. I also prove that the general conjecture follows from a simple combinatorial statement for which substantial computer verification has been obtained.
19 pages, rich supply of figures. This is half of my thesis, "Combinatorics of degeneracy loci"
19 pages, rich supply of figures. This is half of my thesis, "Combinatorics of degeneracy loci"