Theta Correspondence of Automorphic Characters

dc.creatorSnitz, Kobi
dc.date2005-09-21
dc.date.accessioned2026-07-07T06:18:33Z
dc.date.available2026-07-07T06:18:33Z
dc.descriptionThis 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.identifierhttps://arxiv.org/abs/math/0509486
dc.identifierhttp://arxiv.org/abs/math/0509486
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94771
dc.subjectNumber Theory
dc.subjectRepresentation Theory
dc.subject11F30;11F27
dc.titleTheta Correspondence of Automorphic Characters
dc.typetext

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