2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155904In 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.36 pages. Corrected version for publicationQuantum AlgebraMathematical PhysicsCombinatoricsRepresentation Theory17B80text