Degenerate rotor manifold without a first-order Stark shift
= Degenerate rotor manifold without a first-order Stark shift
Every state in a fixed-$J$ manifold has <parity> $(-1)^J$, while the dipole component is odd. Therefore its complete matrix within that degenerate manifold vanishes. One must check the whole degenerate block, not only one diagonal element, before concluding that first-order splitting is absent.