  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.
