On simple modules of cyclotomic quiver Hecke algebras of type A

TL;DR

This paper classifies graded simple modules of cyclotomic quiver Hecke algebras of type A using diagram calculus, providing a field-independent lower bound for their dimensions.

Contribution

It introduces a classification method for simple modules of these algebras and establishes a new lower bound on their dimensions.

Findings

Classification of simple modules using diagram calculus

Field-independent lower bound for module dimensions

Enhanced understanding of algebra representations

Abstract

We give a classification of the graded simple modules of cyclotomic quiver Hecke algebras of type A using the diagram calculus of the diagrammatic Cherednik algebra. We also obtain a non-trivial lower bound for the dimension of the simple modules which is independent of the field characteristic.