Path description for $q$-characters of fundamental modules in type $C$
Abstract
In this paper, we investigate the behavior of monomials in the -characters of the fundamental modules over a quantum affine algebra of untwisted type C. As a result, we give simple closed formulae for the -characters of the fundamental modules in terms of sequences of vertices in , so-called paths, with an admissible condition. This may be viewed as a type C analog of the path description of -characters in types A and B due to Mukhin--Young.
Keywords
Cite
@article{arxiv.2211.03303,
title = {Path description for $q$-characters of fundamental modules in type $C$},
author = {Il-Seung Jang},
journal= {arXiv preprint arXiv:2211.03303},
year = {2025}
}
Comments
v4: minor revision; v3: 23 pages, revised introduction and abstract, reference added, comments added on Remark 2.1, 3.1, 3.2, 4.5, 4.9, 4.10, added Section 4.2 to explain connected components, added Examples 2.4, 4.4, added Lemma 4.6, revised proof of Theorem 4.7, and several typos corrected; v2: 15 pages, typos corrected, reference corrected