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POSITIVITY OF EQUIVARIANT GROMOV-WITTEN DAVE ANDERSON AND LINDA CHEN
 

Summary: POSITIVITY OF EQUIVARIANT GROMOV-WITTEN
INVARIANTS
DAVE ANDERSON AND LINDA CHEN
Abstract. We show that the equivariant Gromov-Witten invariants of
a projective homogeneous space G/P exhibit Graham-positivity: 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) = B-wP/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

  

Source: Anderson, Dave - Department of Mathematics, University of Washington at Seattle

 

Collections: Mathematics