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

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

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Universal graded Specht modules for cyclotomic Hecke algebras (2011, methodology): “23 when we show that these universal graded Specht modules are isomorphic to the usual graded Specht modules from [6, 10].”
Crystals from categorified quantum groups (2009, background): “This has led to the definition of graded Specht modules for cyclotomic Hecke algebras [11], the construction of a homogeneous cellular basis for the cyclotomic quotients R(ν) in type A [22], the introduction of gradings in the study of q-Schur algebras [4], and an extension of the generalized LLT co”
The $\mathfrak{sl}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality (2014, methodology): “Additionally, during the final preparation of this paper, the authors became aware of the preprint [51], in which Tubbenhauer uses categorical skew Howe duality to present an explicit basis for Mackaay’s sln web algebra, by adapting the HuMathas basis for the cyclotomic KLR algebra [18].”
Representation theory of symmetric groups and related Hecke algebras (2009, unknown): “One way to approach them is via Specht modules, which will be discussed in the next section.”