The q-characters at roots of unity

We consider various specializations of the non-twisted quantum affine algebras at roots of unity. We define and study the q-characters of their finite-dimensional representations.Comment: 22 pages, Late

Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras

We study finite-dimensional representations of quantum affine algebras using q-characters. We prove the conjectures from math.QA/9810055 and derive some of their corollaries. In particular, we prove that the tensor product of fundamental representations is reducible if and only if at least one of the corresponding normalized R-matrices has a pole.Comment: 35 pages, Late

Extended TT-System of Type G2G_2

We prove a family of 3-term relations in the Grothendieck ring of the category of finite-dimensional modules over the affine quantum algebra of type $G_2$ extending the celebrated $T$-system relations of type $G_2$. We show that these relations can be used to compute classes of certain irreducible modules, including classes of all minimal affinizations of type $G_2$. We use this result to obtain explicit formulas for dimensions of all participating modules