# On multiplicity-free weight modules over quantum affine algebras

## TL;DR

This paper constructs and analyzes multiplicity-free weight modules over quantum affine algebras, introducing shiftability conditions and computing their highest $\

## Contribution

It introduces the shiftability condition and provides a new framework for understanding infinite-dimensional multiplicity-free modules.

## Key findings

- Defined shiftability condition for quantum affine algebras
- Constructed infinite-dimensional multiplicity-free weight modules
- Computed highest $\

## Abstract

In this note, our goal is to construct and study the multiplicity-free weight modules of quantum affine algebras. For this, we introduce the notion of shiftability condition with respect to a symmetrizable generalized Cartan matrix, and investigate its applications on the study of quantum affine algebra structures and the realizations of the infinite-dimensional multiplicity-free weight modules. We also compute the highest $\ell$-weights of the infinite-dimensional multiplicity-free weight modules as highest $\ell$-weight modules.