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Cuspidal systems parameterize KLR algebra representations via root partitions, where simple modules L () arise as heads of proper standard modules. Working in affine type A with an arbitrary convex preorder, we construct explicit skew diagrams () such that the skew Specht module S^ () has simple head L () and a filtration by proper standard modules. This result arises from an in-depth study of the combinatorial interplay between cuspidal systems and RoCK cyclotomic KLR algebras.
Muth et al. (Fri,) studied this question.