Graded Skew Specht Modules and Cuspidal Modules for Khovanov-Lauda-Rouquier Algebras of Affine Type A

Kleshchev, Mathas and Ram. Proc. Lond. Math. Soc. (2) 105, 1245-1289 (2012) gave a presentation for graded Specht modules over Khovanov-Lauda-Rouquier algebras of finite and affine type A. We show that this construction can be applied more generally to skew shapes to give a presentation of graded skew Specht modules, which arise as subquotients of restrictions of Specht modules. As an application, we show that cuspidal modules associated to a balanced convex preorder in affine type A are skew Specht modules for certain hook shapes.