Does anyone have read their famous paper'the moment map and equivariant cohomology'. I may find  some error in it . IN the original paper page 13,the equalities between (4.18)and (4.19) is $D\lambda a=D(a-i(X)a\theta)=da-i(X)da \theta + i(X)au$ , i think  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!