We present identities relating the pair-correlation functions and static structure factors of states in the maximal spin multiplet. This allows us to compute these density-density correlation functions of all members of the multiplet using just these correlation functions of the highest-weight state. We apply these relations to obtain energies for many fractional quantum Hall (FQH) states. In particular, we analytically compute the energies of the Halperin-(1,1,1) state as a function of density imbalance and layer separation, and numerically evaluate these energies for many other FQH states.

Ref: arXiv:2604.22628