Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A
| dc.contributor.advisor | Kleshchev, Alexander | |
| dc.contributor.author | Loubert, Joseph | |
| dc.date.accessioned | 2015-08-18T23:02:53Z | |
| dc.date.available | 2015-08-18T23:02:53Z | |
| dc.date.issued | 2015-08-18 | |
| dc.description.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. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/19255 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | Creative Commons BY 4.0-US | |
| dc.subject | Affine cellularity | en_US |
| dc.subject | KLR algebras | en_US |
| dc.subject | Specht modules | en_US |
| dc.title | Affine Cellularity of Finite Type KLR Algebras, and Homomorphisms Between Specht Modules for KLR Algebras in Affine Type A | |
| dc.type | Electronic Thesis or Dissertation | |
| thesis.degree.discipline | Department of Mathematics | |
| thesis.degree.grantor | University of Oregon | |
| thesis.degree.level | doctoral | |
| thesis.degree.name | Ph.D. |
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