  Nakajima introduced the morphism of q,t-characters for finite dimensional
representation of simply-laced quantum affine algebras : it is a t-deformation
of the Frenkel-Reshetikhin's morphism of q-characters (sum of monomials in
infinite variables). In math.QA/0212257 we generalized the construction of
q,t-characters for non simply-laced quantum affine algebras. First in this
paper we prove a conjecture of math.QA/0212257 : the monomials of q and
q,t-characters of standard representations are the same in non simply-laced
cases (the simply-laced cases were treated by Nakajima) and the coefficients
are non negative. In particular these q,t-characters can be considered as
t-deformations of q-characters. In the proof we show that for quantum affine
algebras of type A, B, C and quantum toroidal algebras of type A^{(1)} the
l-weight spaces of fundamental representations are of dimension 1. Eventually
we show and use a generalization of results of Frenkel-Reshetikhin, -Mukhin and
Nakajima : for general quantum affinizations we prove that the l-weights of a
l-highest weight simple module are lower than the highest l-weight in the sense
of monomials.
