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 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.