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.
| Identifer | oai:union.ndltd.org:uoregon.edu/oai:scholarsbank.uoregon.edu:1794/19255 |
| Date | 18 August 2015 |
| Creators | Loubert, Joseph |
| Contributors | Kleshchev, Alexander |
| Publisher | University of Oregon |
| Source Sets | University of Oregon |
| Language | en_US |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Rights | Creative Commons BY 4.0-US |
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