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
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.
Received: 15 January 2008
Revised: 24 April 2008
First available in Project Euclid: 24 November 2018
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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