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Title Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A
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Publication Date
Date Accessioned
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
Date Indexed 2020-06-18
Grantor University of Oregon
Issued Date 2015-08-18 00:00:00

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