Date of Completion
Khovanov-Lauda-Rouquier Algebras, KLR Algebras, Homogeneous Representations, Fully Commutative Elements
Field of Study
Doctor of Philosophy
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.
Feinberg, Gabriel, "Homogeneous Representations of Khovanov-Lauda-Rouquier Algebras" (2013). Doctoral Dissertations. 118.