On a conjectured formula for quiver varieties
Abstract
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.
Cite
@article{arxiv.math/9909089,
title = {On a conjectured formula for quiver varieties},
author = {Anders S. Buch},
journal= {arXiv preprint arXiv:math/9909089},
year = {2007}
}
Comments
19 pages, rich supply of figures. This is half of my thesis, "Combinatorics of degeneracy loci"