On q, t-characters and the l-weight Jordan Filtration of Standard Uq(Ŝl₂)-modules

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)