Path description for q-characters of fundamental modules in type C

Abstract

In this paper, we investigate the behavior of monomials in the q-characters of the fundamental modules over a quantum affine algebra of untwisted type C. As a result, we give simple closed formulae for the q-characters of the fundamental modules in terms of sequences of vertices in ${\mathbb{R}}^2$, so-called paths, with an admissible condition. This may be viewed as a type C analog of the path description of q-characters in types A and B due to Mukhin–Young.

KEYWORDS:

• Fundamental modules
• path descriptions
• q-characters
• quantum affine algebras

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B37
• 17B65
• 05E10

Acknowledgments

The author would like to thank Se-jin Oh for many stimulating and helpful discussions; to Sin-Myung Lee for his valuable comments. He also would like to thank sincerely the anonymous referee for helpful and detailed comments.

Notes

1 https://sites.google.com/view/isjang/side-project/hernandez-leclerc-algorithm-for-q-characters

2 https://github.com/ILSEUNGJANG/Algorithms/blob/main/HLalgorithm/Examples/qchar_graphs.pdf

Additional information

Funding

This work was supported by Incheon National University Research Grant in 2022 (No. 2022-0379).