X=M for symmetric powers

The X=M conjecture of Hatayama et al. asserts the equality between the one-dimensional configuration sum X expressed as the generating function of crystal paths with energy statistics and the fermionic formula M for all affine Kac–Moody algebras. In this paper we prove the X=M conjecture for tensor products of Kirillov–Reshetikhin crystals B1,s associated to symmetric powers for all nonexceptional affine algebras.