Explicit formulas for q-characters of arbitrary simple modules

Derive explicit formulas for the q-characters of arbitrary simple finite-dimensional modules over the quantum affine algebra U_q(ĝ).

Background

The paper highlights that while q-characters are a powerful tool for studying finite-dimensional representations of quantum affine algebras, general explicit formulas beyond special cases are not currently available. Existing results include the highest monomial property and algorithms for fundamental representations, but a complete closed-form description for arbitrary simple modules is lacking.

The authors develop new structures—most notably, the extremal monomial property and X-series—to approach these structural questions and link q-characters to integrable models, suggesting a pathway to eventual resolution.