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 Author Loubert, Joseph Title Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A URL http://hdl.handle.net/1794/19255 Publication Date 2015 Date Accessioned 2015-08-18 23:02:53 Degree PhD Discipline/Department Department of Mathematics Degree Level doctoral University/Publisher University of Oregon Abstract This thesis consists of two parts. In the first we prove that the Khovanov-Lauda-Rouquier algebras $R_\alpha$ of finite type are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals in $R_\alpha$ are generated by idempotents. This in particular implies the (known) result that the global dimension of $R_\alpha$ is finite. In the second part we use the presentation of the Specht modules given by Kleshchev-Mathas-Ram to derive results about Specht modules. In particular, we determine all homomorphisms from an arbitrary Specht module to a fixed Specht module corresponding to any hook partition. Along the way, we give a complete description of the action of the standard KLR generators on the hook Specht module. This work generalizes a result of James. This dissertation includes previously published coauthored material. Subjects/Keywords Affine cellularity; KLR algebras; Specht modules Contributors Kleshchev, Alexander (advisor) Language en Rights Creative Commons BY 4.0-US [Always confirm rights and permissions with the source record.] Country of Publication us Record ID handle:1794/19255 Repository oregon Date Retrieved 2020-06-15 Date Indexed 2020-06-18 Grantor University of Oregon Issued Date 2015-08-18 00:00:00

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…x29; when λ is a hook. Affine Cellularity of KLR Algebras of Finite Types The content of chapter II has already been published as (18). The goal of chapter II is to establish (graded) affine cellularity in the sense of Koenig and Xi…

…graded) cellularity of cyclotomic KLR algebras of finite types. Our approach is independent of the homological results in (30), (13) and (3) (which relies on (30)). The connection between the theory…

cellularity. We begin in subsection 2.2 by choosing some special word idempotents and proving some properties they enjoy. Subsection 2.2 introduces the notation that allows us to define our affine cellular structure. This subsection also contains the crucial…

…Specht module S µ to S λ , where λ is a hook. In section 6, we consider some examples. 10 CHAPTER II AFFINE CELLULARITY OF KLR ALGEBRAS The content of this chapter has already been published as (18). Preliminaries and a Dimension Formula In…