Modules with Good Filtrations over Generalized Schur Algebras
| dc.contributor.advisor | Kleshchev, Alexander | |
| dc.contributor.author | Weinschelbaum, Ilan | |
| dc.date.accessioned | 2022-10-04T19:27:54Z | |
| dc.date.available | 2022-10-04T19:27:54Z | |
| dc.date.issued | 2022-10-04 | |
| dc.description.abstract | In this dissertation we examine generalized Schur algebras, as defined by Kleshchev and Muth. Given a quasi-hereditary superalgebra $A$, Kleshchev and Muth proved that for $n \geq d$, the generalized Schur algebra $T^A (n,d)$ is again quasi-hereditary.They described the bisuperalgebra struture on $T^A(n) := \bigoplus_d T^A(n,d)$. In particular, there is a coproduct which gives us a way to take a $T^A(n,d)$-module $V$ and $T^A(n,r)$-module $W$ and produce a $T^A(n,d+r)$-module $V \otimes W$. We will prove that if $V$ and $W$ each have standard (resp. costandard) filtrations, then so does $V \otimes W$. In the last chapter we will use this result to prove that in the case that $A$ is the extended zigzag algebra $\EZig$, the extended zigzag Schur algebra $T^\EZig(n,d)$ is Ringel self-dual for all $n \geq d$. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/27551 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | All Rights Reserved. | |
| dc.subject | Algebra | en_US |
| dc.subject | Highest Weight Categories | en_US |
| dc.subject | Quasi-Hereditary Algebras | en_US |
| dc.subject | Representation Theory | en_US |
| dc.subject | Schur Algebras | en_US |
| dc.title | Modules with Good Filtrations over Generalized Schur Algebras | |
| 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. |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- Weinschelbaum_oregon_0171A_13254.pdf
- Size:
- 667.65 KB
- Format:
- Adobe Portable Document Format