On the restriction of representations of $\GL_2(F)$ to a Borel subgroup
| dc.creator | Paskunas, Vytautas | |
| dc.date | 2006-10-04 | |
| dc.date.accessioned | 2026-07-07T07:28:42Z | |
| dc.date.available | 2026-07-07T07:28:42Z | |
| dc.description | Let $F$ be a non-Archimedean local field and let $p$ be the residual characteristic of $F$. Let $G=GL_2(F)$ and let $P$ be a Borel subgroup of $G$. In this paper we study the restriction of irreducible representations of $G$ on $E$-vector spaces to $P$, where $E$ is an algebraically closed field of characteristic $p$. We show that in a certain sense $P$ controls the representation theory of $G$. We then extend our results to smooth $\oK[G]$- modules of finite length and unitary $K$-Banach space representations of $G$, where $\oK$ is the ring of integers of a complete discretely valued field $K$, with residue field $E$. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610156 | |
| dc.identifier | http://arxiv.org/abs/math/0610156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117831 | |
| dc.subject | Representation Theory | |
| dc.subject | Number Theory | |
| dc.subject | 22E50 | |
| dc.title | On the restriction of representations of $\GL_2(F)$ to a Borel subgroup | |
| dc.type | text |