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

2023/05/23 by Tong, Jun, Duan, Bing, Luo, Yanfeng · 1 citation
#Combinatorics #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra #Quantum Algebra (math.QA) #Representation Theory #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2305.13671

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.

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