  In this paper we give a direct proof of the equality of certain generating
function associated with tensor product multiplicities of Kirillov-Reshetikhin
modules 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.
