Representations of Partition Categories
| dc.contributor.advisor | Brundan, Jonathan | |
| dc.contributor.author | Vargas, Max | |
| dc.date.accessioned | 2023-07-06T14:01:43Z | |
| dc.date.available | 2023-07-06T14:01:43Z | |
| dc.date.issued | 2023-07-06 | |
| dc.description.abstract | We explain a new approach to the representation theory of the partition category based on a reformulation of the definition of the Jucys-Murphy elements introduced originally by Halverson and Ram and developed further by Enyang. Our reformulation involves a new graphical monoidal category, the affine partition category, which is defined here as a certain monoidal subcategory of Khovanov's Heisenberg category. We use the Jucys-Murphy elements to constructsome special projective functors, then apply these functors to give self-contained proofs of results of Comes and Ostrik on blocks of Deligne’s category $\REP(S_t)$. We then study a restriction functor $\REP(S_t)\to\REP(S_{t-1})$ and prove a conjecture of Comes and Ostrik involving this functor. Finally, we use the restriction functor to verify a criterion of Benson, Etingof, and Ostrik, thereby identifying the abelian envelope of $\REP(S_t)$ with the Ringel dual of the category of locally finite-dimensional $\Par_t$-modules. This dissertation includes published co-authored material. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/28487 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | All Rights Reserved. | |
| dc.title | Representations of Partition Categories | |
| 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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