Again the same paper:
https://projecteuclid.org/euclid.cmp/1103858969
On page 104, they argue that Eq. (6.4) follows immediately from (6.3) on page 103 and (E1) on page 102, with V replaced by ˉU, because Λ(U,ˉU) leaves the zero component invariant.
Here are the equations:
(E1)σνk(x1,…,xn)=∑μSk(U−1,V−1)μνσμk(Rx1+a,…,Rxn+a)
(6.3)Sνk(ξ1,…,ξn)=∫e−∑nk=1(ξ0kq0k−iξkqk)˜W(q1,…,qn)d4nq
I don't see how this is immediate, can someone clear this matter to me?