On q,t-characters and the l-weight Jordan filtration of standard quantum affine sl2 modules

TL;DR

This paper investigates the Jordan filtration of standard modules of quantum affine sl2, linking the filtration's structure to the t-dependence of q,t-characters and providing explicit bases for analysis.

Contribution

It establishes a direct connection between Jordan grades and q,t-characters for all standard quantum affine sl2 modules, with explicit basis constructions.

Findings

Dimensions of Jordan grades derived from q,t-characters

Explicit bases constructed for standard modules

Jordan filtration structure characterized for all standard modules

Abstract

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).