## Advanced Studies in Pure Mathematics

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

#### 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.

#### Article information

Dates
Revised: 24 April 2008
First available in Project Euclid: 24 November 2018

https://projecteuclid.org/ euclid.aspm/1543085351

Digital Object Identifier
doi:10.2969/aspm/06110327

Mathematical Reviews number (MathSciNet)
MR2867151

Zentralblatt MATH identifier
1241.81108

#### Citation

Nakai, Wakako; Nakanishi, Tomoki. On Frenkel–Mukhin algorithm for $q$-character of quantum affine algebras. Exploring New Structures and Natural Constructions in Mathematical Physics, 327--347, Mathematical Society of Japan, Tokyo, Japan, 2011. doi:10.2969/aspm/06110327. https://projecteuclid.org/euclid.aspm/1543085351