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.identifier.uri |
http://hdl.handle.net/1794/19255 |
|
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.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.name |
Ph.D. |
|
thesis.degree.level |
doctoral |
|
thesis.degree.discipline |
Department of Mathematics |
|
thesis.degree.grantor |
University of Oregon |
|