# Classification of prime modules of quantum affine algebras corresponding to 2-column tableaux

## TL;DR

This paper classifies prime modules of quantum affine algebras related to 2-column tableaux and proposes a condition for modules with more columns.

## Contribution

The paper provides a classification of prime modules for 2-column tableaux and a conjectural condition for larger tableaux.

## Key findings

- All prime modules for 2-column semistandard Young tableaux are classified.
- A conjectural sufficient condition for primality in tableaux with more than two columns is proposed.

## Abstract

Finite-dimensional simple modules of quantum affine algebras of type A correspond to semistandard Young tableaux of rectangular shapes. In this paper, we classify all prime modules corresponding to 2-column semistandard Young tableaux, up to a conjectural property. Moreover, we give a conjectural sufficient condition for a module corresponding to a tableau with more than two columns to be prime.