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.
Recommended Citation
Feinberg, Gabriel, "Homogeneous Representations of Khovanov-Lauda-Rouquier Algebras" (2013). Doctoral Dissertations. 118.
https://digitalcommons.lib.uconn.edu/dissertations/118