On Frenkel-Mukhin algorithm for q-character of quantum affine algebras
arXiv:0801.2239
Abstract
The q-character is a strong tool to study finite-dimensional representations of quantum affine algebras. However, the explicit formula of the q-character of a given representation has not been known so far. Frenkel and Mukhin proposed the iterative algorithm which generates the q-character of a given irreducible representation starting from its highest weight monomial. The algorithm is known to work for various classes of representations. In this note, however, we give an example in which the algorithm fails to generate the q-character.
19 pages, minor corrections (Remark 3.1, Eq (3.11), etc); final version to appear in Adv. Stud. in Pure Math., the proceedings volume for the workshop "Exploration of New Structures and Natural Constructions in Mathematical Physics", Nagoya, 2007