Faculty (2004)

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 algebra. In
this paper we prove the X=M conjecture for tensor products of Kirillov--Reshetikhin
crystals B^{1,s} associated to symmetric powers for all nonexceptional affine algebras.