Has anyone read their famous paper 'The moment map and equivariant cohomology'. I may have found some error in it . In the original paper page 13, the equalities between (4.18) and (4.19) $D\lambda a=D(a-i(X)a\theta)=da-i(X)da \theta + i(X)au$ may have something wrong, it should be $D\lambda a=D(a-i(X)a\theta)=da+i(X)da\theta + i(X)au$ where the minus is killed by $\mathcal{L}(X)=i(X)d+di(X)$, so if it is really wrong, the following in their paper may not be very as it be in the paper!