Path description of type B q-characters

TL;DR

This paper provides explicit path descriptions for q-characters of certain modules in type B quantum affine groups, confirming a conjecture and offering a new characterization method.

Contribution

It introduces sufficient conditions for Laurent polynomials to be q-characters and applies them to describe q-characters in type B, proving a conjecture.

Findings

Explicit path description of q-characters for type B modules

Confirmation of Kuniba-Ohta-Suzuki conjecture

Sufficient conditions for Laurent polynomials to be q-characters

Abstract

We give a set of sufficient conditions for a Laurent polynomial to be the q-character of a finite-dimensional irreducible representation of a quantum affine group. We use this result to obtain an explicit path description of q-characters for a class of modules in type B. In particular, this proves a conjecture of Kuniba-Ohta-Suzuki.