X=M for symmetric powers
arXiv:math/0412376 · doi:10.1016/j.jalgebra.2005.04.023
Abstract
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.
40 pages; to appear in J. Algebra