Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A

TL;DR

This paper constructs an explicit homogeneous cellular basis for cyclotomic Khovanov--Lauda--Rouquier algebras of type A, providing a new algebraic framework for understanding their structure.

Contribution

It introduces a novel explicit homogeneous cellular basis for these algebras, advancing the algebraic understanding of their representations.

Findings

Established a cellular basis for cyclotomic KLR algebras of type A.

Facilitated new insights into their module categories.

Enhanced tools for studying categorification and related algebraic structures.

Abstract

This paper constructs an explicit homogeneous cellular basis for the cyclotomic Khovanov--Lauda--Rouquier algebras of type $A$.