Positivity in equivariant quantum Schubert calculus

Abstract. A conjecture of D. Peterson, proved by W. Graham, states that the structure constants of the (T-)equivariant cohomology of a homogeneous space G/P satisfy a certain positivity property. In this paper we show that this positivity property holds in the more general situation of equivariant quantum cohomology. 1. Introduction. It is well known that the (integral) cohomology of the homogeneous space X = G/P (for G a connected, semisimple, complex Lie group and P a parabolic subgroup) satisfies a positivity property: its structure constants are nonnegative integers equal to the number of intersection points of three Schubert varieties, in general position, whose codimensions add up to th