Date of Completion

5-3-2016

Embargo Period

4-29-2016

Keywords

Representation Theory, KLR Algebras

Major Advisor

Kyu-Hwan Lee

Associate Advisor

Ralf Schiffler

Associate Advisor

Jerzy Weyman

Field of Study

Mathematics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

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.

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