Restricting supercharacters of the finite group of unipotent uppertriangular matrices
| dc.creator | Thiem, Nathaniel | |
| dc.creator | Venkateswaran, Vidya | |
| dc.date | 2007-12-07 | |
| dc.date.accessioned | 2026-07-07T08:48:05Z | |
| dc.date.available | 2026-07-07T08:48:05Z | |
| dc.description | It is well-known that the representation theory of the finite group of unipotent upper-triangular matrices $U_n$ over a finite field is a wild problem. By instead considering approximately irreducible representations (supercharacters), one obtains a rich combinatorial theory analogous to that of the symmetric group, where we replace partition combinatorics with set-partitions. This paper studies the supercharacter theory of a family of subgroups that interpolate between $U_{n-1}$ and $U_n$. We supply several combinatorial indexing sets for the supercharacters, supercharacter formulas for these indexing sets, and a combinatorial rule for restricting supercharacters from one group to another. A consequence of this analysis is a Pieri-like restriction rule from $U_n$ to $U_{n-1}$ that can be described on set-partitions (analogous to the corresponding symmetric group rule on partitions). | |
| dc.identifier | https://arxiv.org/abs/0712.1237 | |
| dc.identifier | http://arxiv.org/abs/0712.1237 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143825 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | Group Theory | |
| dc.subject | 20C99 | |
| dc.title | Restricting supercharacters of the finite group of unipotent uppertriangular matrices | |
| dc.type | text |