Irreducibility of \bar{M}_{0,n}(G/P,β)

Let G be a linear algebraic group, P be a parabolic subgroup of G and \beta be a cycle of dimension 1 in the Chow group of the quotient G/P. Using geometric arguments and Borel's fixed point theorem, we prove that the moduli space \bar{M}_{0,n}(G/P, \beta) of n-pointed genus 0 stable maps representing \beta is irreducible.