Date of Completion
Representation Theory, KLR Algebras
Field of Study
Doctor of Philosophy
The module categories of Khovanov-Lauda-Rouquier algebras categorify the integral form of the negative half of the quantum group U_q(g) coming from any symmetrizable Kac-Moody algebra g. We construct a family of simple modules over KLR algebras and show how they can be used to obtain the building blocks of existing classifications of simple finite-dimensional modules in finite types. The construction extends to infinite types, where we obtain simple modules whose structures are easy to describe. We give many explicit examples of this construction in rank 2 cases.
Judge, Jonathan Brian, "Modules Over Rank 2 KLR Algebras" (2016). Doctoral Dissertations. 1089.