A combinatorial model for q-characters of fundamental modules of type Dn

Abstract

In this paper, we introduce a combinatorial path model of representation of the quantum affine algebra of type D n , inspired by Mukhin and Young’s combinatorial path models of representations of the quantum affine algebras of types A n and B n . In particular, we give a combinatorial formula for q-characters of fundamental modules of type D n by assigning each path to a monomial or binomial. By counting our paths, a new expression on dimensions of fundamental modules of type D n is obtained.