On Frenkel-Mukhin algorithm for q-character of quantum affine algebras

Details On Frenkel-Mukhin algorithm for q-character of quantum affine algebras On Frenkel-Mukhin algorithm for q-character of quantum affine algebras

2008-01-15

arxiv.org/abs/0801.2239v2

Adv. Stud. Pure Math. 61 (2011) 327--347

Mathematics

Quantum Algebra

19 pages, minor corrections (Remark 3.1, Eq (3.11), etc); final version to appear in Adv. Stud. in Pure Math., the proceedings

Scientific paper

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.

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