Date of Completion

8-4-2016

Embargo Period

8-4-2016

Keywords

KLR algebra

Major Advisor

Kyu-Hwan Lee

Associate Advisor

Jerzy Weyman

Associate Advisor

Ralf Schiffler

Field of Study

Mathematics

Degree

Doctor of Philosophy

Open Access

Campus Access

Abstract

We study convex order and a cuspidal system for the Khovanov-Lauda-Rouquier (KLR) algebras of twisted affine type. This allows us to classify the irreducible modules over KLR algebras of twisted affine type. Particularly, we are interested in the imaginary modules. They can be constructed from the colored minuscule imaginary modules. We describe explicitly minuscule imaginary modules of certain colors for the Cartan matrices . Moreover, we discuss the the relation between the dimension of minuscule imaginary modules of color and Catalan numbers. For untwisted affine types, Kleshchev and Muth showed that the square of a certain permutation on the imaginary tensor space of a fixed color is a nonzero map. However, it is not the case for twisted affine types. We present a new result that these maps of the imaginary tensor spaces of certain color for some twisted affine types are equal to zero

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