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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
Article
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Abstract

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.

Keywords

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

Mathematics Subject Classification (2010)

20C08 20C30 05E10 

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Notes

Acknowledgments

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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