Date of Completion

5-7-2013

Embargo Period

5-7-2013

Keywords

Khovanov-Lauda-Rouquier Algebras, KLR Algebras, Homogeneous Representations, Fully Commutative Elements

Major Advisor

Kyu-Hwan Lee

Associate Advisor

Alvaro Lozano-Robledo

Associate Advisor

Ralf Schiffler

Field of Study

Mathematics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

The Khovonov-Lauda-Rouquier (KLR) algebra arose out of attempts to categorify quantum groups. Kleshchev and Ram proved a result reducing the representation theory of these algebras to the study of irreducible cuspidal representations. In finite types, these cuspidal representations are part of a larger class of homogeneous representations, which are related to fully commutative elements of Coxeter groups.

For KLR algebras of types An and Dn, we classify and enumerate these homogeneous representations.

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