The University of Michigan Combinatorics Seminar


Abstract 

Let Hom(V) be the set of quivers
V_{0} > V_{1} > ... > V_{n}.
A quiver cycle is a subset O_{r} of Hom(V)
where the ranks of the composite maps
V_{i} > V_{j} are
bounded above by specified integers r=(r_{ij})
for i < j .
Our goal is to compute the equivariant cohomology class
[O_{r}].
As a special case one obtains Fulton's universal Schubert polynomials.
Buch and Fulton expressed [O_{r}] in
terms of Schur functions, and conjectured
a combinatorial formula for the coefficients.
In particular, they conjectured that the coefficients, which directly
generalize the
LittlewoodRichardson coefficients, are positive. 