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

TL;DR

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

Contribution

It provides a complete classification for 2-column tableaux modules and introduces a conjectural condition for prime modules with more columns.

Findings

Classified all prime modules for 2-column tableaux.

Proposed a conjectural criterion for modules with more than two columns.

Connected module classification to combinatorial tableau structures.

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.