商$\Q^\times\ltimes\Q\bs\A^1\ltimes \A$的调和分析
Harmonic Analysis on the quotient $\Q^\times\ltimes\Q\bs\A^1\ltimes \A$
摘要：
设$G$是模与模1的半直积$\A^1\ltimes \A$.令$\Ga$为离散子群$\Q^\times\ltimes\Q$。本文建立了这种情况下的迹公式，并利用它给出了$L^2(\Ga\bs G)$上的$G$ -表示的完全分解。证明了范数为1的Idele类群的特征标都给出一个一维的同构，并且这些同构的补由一个不可约表示组成。
英文摘要：
Let $G$ be the semidirect product $\A^1\ltimes \A$ of the adeles and the norm 1 ideles. Let $\Ga$ be the discrete subgroup $\Q^\times\ltimes\Q$. In this paper the trace formula for this setting is established and used to give the complete decomposition of the $G$-representation on $L^2(\Ga\bs G)$. It turns out that every character of the norm-1 idele class group gives a one dimensional isotype and the complement of those consists of one irreducible representation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
