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

TL;DR

This paper provides a new combinatorial path description for the $q$-characters of fundamental modules in quantum affine algebras of type C, extending previous type A and B results.

Contribution

It introduces simple closed formulas for $q$-characters of fundamental modules in type C using path sequences, offering a novel combinatorial approach.

Findings

Closed formulae for $q$-characters in type C

Path description using vertices in $\\mathbb{R}^2$

Extension of type A and B path descriptions

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.