  We study the ground state orbital ordering of $LaMnO_3$, at weak
electron-phonon coupling, when the spin state is A-type antiferromagnet. We
determine the orbital ordering by extending to our Jahn-Teller system a
recently developed Peierls instability framework for the Holstein model [1]. By
using two-dimensional dynamic response functions corresponding to a mixed
Jahn-Teller mode, we establish that the $Q_2$ mode determines the orbital
order.
