Intersection multiplicity one for classical groups

In this paper we show that when $\mathrm{G}$ is a classical semi-simple algebraic group, $\mathrm{B}\subset \mathrm{G}$ a Borel subgroup, and $\mathrm{X}=\mathrm{G}\mathrm{/}\mathrm{B}$, then the structure coefficients of the Belkale-Kumar product ${\odot }_0$ on ${\mathrm{H}}^{\ast }(\mathrm{X},\mathbf{Z})$ are all either $0$ or $1$.