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- W2953011005 abstract "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 $I_{V}(chi,phi)$ determined by the Schwartz function $phiin Sc(V(A))$ in the lift of the character $chi$ we match an automorphic form $I_{U}(mu,phi_{0})$ determined by the Schwartz function $phi_{0}in Sc(U(A))$ in the lift of the character $mu$. Our work shows that, the space $U$ is explicitly determined by the character $chi$. The character $mu$ is explicitly determined by the space $V$ and the function $phi_{0}$ is given by an orbital integral involving $phi$." @default.
- W2953011005 created "2019-06-27" @default.
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- W2953011005 date "2005-09-21" @default.
- W2953011005 modified "2023-09-27" @default.
- W2953011005 title "Theta Correspondence of Automorphic Characters" @default.
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