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Irreducible Modules over KLR Algebras of Twisted Affine Type

By Tze-Chun Ou

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 zer

Topics: KLR algebra
Publisher: OpenCommons@UConn
Year: 2016
OAI identifier: oai:opencommons.uconn.edu:dissertations-7445
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