A skew Specht perspective of RoCK blocks and cuspidal systems for KLR algebras in affine type A

Cuspidal systems parameterize KLR algebra representations via root partitions π, where simple modules L(π) arise as heads of proper standard modules. Working in affine type A with an arbitrary convex preorder, we construct explicit skew diagrams ζ(π) such that the skew Specht module Sζ(π) has simple head L(π) 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.