 
Summary: POSITIVITY OF EQUIVARIANT GROMOVWITTEN
INVARIANTS
DAVE ANDERSON AND LINDA CHEN
Abstract. We show that the equivariant GromovWitten invariants of
a projective homogeneous space G/P exhibit Grahampositivity: when
expressed as polynomials in the positive roots, they have nonnegative
coefficients.
1. Introduction
Let X = G/P be a projective homogeneous variety, for a complex reduc
tive Lie group G and parabolic subgroup P. Fix a maximal torus and Borel
subgroup T B P, and let = {1, . . . , n} be the corresponding set
of simple roots, making the roots of B positive. Let WP W be the Weyl
groups for P and G, respectively. Let B be the opposite Borel subgroup.
The classes of the Schubert varieties X(w) = BwP/P and opposite Schu
bert varieties Y (w) = BwP/P give PoincarŽe dual bases of the equivariant
cohomology ring H
T X, as w ranges over the set WP of minimal coset repre
sentatives for W/WP . Write x(w) = [X(w)]T and y(w) = [Y (w)]T for these
classes.
A positivity property for multiplication in these bases was proved by
