  The Cartan subalgebra of the sl2 quantum affine algebra is generated by a
family of mutually commuting operators, responsible for the l-weight
decomposition of finite dimensional modules. The natural Jordan filtration
induced by these operators is generically non-trivial on l-weight spaces of
dimension greater than one. We derive, for every standard module of quantum
affine sl2, the dimensions of the Jordan grades and prove that they can be
directly read off from the t-dependence of the q,t-characters introduced by
Nakajima. To do so we construct explicit bases for the standard modules with
respect to which the Cartan generators are upper-triangular. The basis vectors
of each l-weight space are labelled by the elements of a ranked poset from the
family L(m,n).
