## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Exploring New Structures and Natural Constructions in Mathematical Physics, K. Hasegawa, T. Hayashi, S. Hosono and Y. Yamada, eds. (Tokyo: Mathematical Society of Japan, 2011), 327 - 347

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

Wakako Nakai and Tomoki Nakanishi

#### 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**

Received: 15 January 2008

Revised: 24 April 2008

First available in Project Euclid:
24 November 2018

**Permanent link to this document**

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