Algebras and Representation Theory

, Volume 22, Issue 4, pp 977–1015 | Cite as

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

  • Robert MuthEmail author


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.


Khovanov-Lauda-Rouquier algebra Hecke algebra Symmetric group Specht module Cuspidal module 

Mathematics Subject Classification (2010)

20C08 20C30 05E10 


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This paper was written under the supervision of Alexander Kleshchev at the University of Oregon. The author would like to thank Dr. Kleshchev for his helpful comments and guidance.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of MathematicsWashington & Jefferson CollegeWashingtonUSA

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