Proof of the Combinatorial Kirillov-Reshetikhin Conjecture

In this paper, we give a direct proof of the equality of certain generatingfunction associated with tensor product multiplicities of Kirillov-Reshetikhin modules of the untwisted Yangian for each simple Lie algebra g. Together with the theorems of Nakajima and Hernandez, this gives the proof of the combinatorial version of the Kirillov-Reshetikhin conjecture, which gives tensor product multiplicities in terms of restricted fermionic summations.