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

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.

KEYWORDS:

• Combinatorial path models
• fundamental modules
• quantum affine algebras
• q-characters
• screening operators

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B37

Acknowledgments

The authors are very grateful to the anonymous referees for their valuable comments and suggestions.

Disclosure statement

The authors declare that they have no conflict of interest.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China (No. 12171213, No. 12001254), Gansu Province Science Foundation for Youths (No. 22JR5RA534) and the Startup Funds in Lanzhou University (No. 561120205).