  We prove the Kirillov-Reshetikhin conjecture for all untwisted quantum affine
algebras : we prove that the character of Kirillov-Reshetikhin modules solve
the Q-system and we give an explicit formula for the character of their tensor
products. In the proof we show that the Kirillov-Reshetikhin modules are
special in the sense of monomials and that their q-characters solve the
T-system (functional relations appearing in the study of solvable lattice
models). Moreover we prove that the T-system can be written in the form of an
exact sequence. For simply-laced cases, these results were proved by Nakajima
with geometric arguments which are not available in general. The proof we use
is different and purely algebraic, and so can be extended uniformly to non
simply-laced cases.
