Theta Correspondence of Automorphic Characters
| dc.creator | Snitz, Kobi | |
| dc.date | 2005-09-21 | |
| dc.date.accessioned | 2026-07-07T06:18:33Z | |
| dc.date.available | 2026-07-07T06:18:33Z | |
| dc.description | This paper describes the lifting of automorphic characters of $\GO(3)(\A)$ to $\SLT(\A)$. It does so by matching the image of this lift with the lift of automorphic characters from $\GO(1)(\A)$ to $\SLT(\A)$. Our matching actually gives a matching of individual automorphic forms, and not just of representation spaces. Let $\V$ be a $3-$ dimensional quadratic vector space and $\U$ a certain $1-$ dimensional quadratic space. To an automorphic form $I_{\V}(χ,ϕ)$ determined by the Schwartz function $ϕ\in \Sc(\V(\A))$ in the lift of the character $χ$ we match an automorphic form $I_{\U}(μ,ϕ_{0})$ determined by the Schwartz function $ϕ_{0}\in \Sc(\U(\A))$ in the lift of the character $μ$. Our work shows that, the space $\U$ is explicitly determined by the character $χ$. The character $μ$ is explicitly determined by the space $\V$ and the function $ϕ_{0}$ is given by an orbital integral involving $ϕ$. | |
| dc.identifier | https://arxiv.org/abs/math/0509486 | |
| dc.identifier | http://arxiv.org/abs/math/0509486 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94771 | |
| dc.subject | Number Theory | |
| dc.subject | Representation Theory | |
| dc.subject | 11F30;11F27 | |
| dc.title | Theta Correspondence of Automorphic Characters | |
| dc.type | text |