论文标题
古典群体的双重下降
Double Descent in Classical Groups
论文作者
论文摘要
令$ {\ bf a} $为数字字段$ f $的ADELE。鉴于自偶有的不可还原，自动形态，尖锐的表示$ \ gl_n（\ ba）$，带有微不足道的中央字符，我们从适当的分裂经典集团$ g $中构建了其完整的倒数图像。我们通过一种新的自动下降方法来做到这一点，即双重下降。该方法源自CAI，Friedberg，Ginzburg和Kaplan \ Cite {CFGK17}的最新一般性整体积分，该积分代表了$ g \ times \ gl_n $的标准$ L $符合。我们的结果对于符号组的双重覆盖也有效。
Let ${\bf A}$ be the ring of adeles of a number field $F$. Given a self-dual irreducible, automorphic, cuspidal representation $τ$ of $\GL_n(\BA)$, with trivial central characters, we construct its full inverse image under the weak Langlands functorial lift from the appropriate split classical group $G$. We do this by a new automorphic descent method, namely the double descent. This method is derived from the recent generalized doubling integrals of Cai, Friedberg, Ginzburg and Kaplan \cite{CFGK17}, which represent the standard $L$-functions for $G\times \GL_n$. Our results are valid also for double covers of symplectic groups.
