论文标题
在立方Shimura升降机至$ pgl（3）$：基本引理
On the Cubic Shimura lift to $PGL(3)$: The Fundamental Lemma
论文作者
论文摘要
经典的Shimura通信将$ SL_2 $的双封面上的自动形式提升到$ PGL_2 $上的自动形式表示。在这里，我们采取关键步骤，以建立一个相对的跟踪公式，该公式将提供新的全球Shimura升降机，从$ SL_3 $的三重盖到$ PGL_3 $，并且还表征了升降机的图像。表征将是通过在自动形态最小表示空间中涉及函数$θ_{so_8} $的函数的不变，用于拆分$ so_8（{\ Mathbb {a}}）$，一致，与2001年的Bump，Friedberg和Ginzburg的2001构想。在本文中，我们首先分析涉及此期间的$ pgl_3（{\ mathbb {a}}）上的全球分布，并表明它是可分解的轨道积分的总和。对于$ sl_3（{\ mathbb {a}}）$的三重封面附加的kuznetsov分布也是如此。然后，我们匹配球形Hecke代数的单位元素的相应局部轨道积分；也就是说，我们建立了基本的引理。
The classical Shimura correspondence lifts automorphic representations on the double cover of $SL_2$ to automorphic representations on $PGL_2$. Here we take key steps towards establishing a relative trace formula that would give a new global Shimura lift, from the triple cover of $SL_3$ to $PGL_3$, and also characterize the image of the lift. The characterization would be through the nonvanishing of a certain global period involving a function in the space of the automorphic minimal representation $Θ_{SO_8}$ for split $SO_8({\mathbb{A}})$, consistent with a 2001 conjecture of Bump, Friedberg and Ginzburg. In this paper, we first analyze a global distribution on $PGL_3({\mathbb{A}})$ involving this period and show that it is a sum of factorizable orbital integrals. The same is true for the Kuznetsov distribution attached to the triple cover of $SL_3({\mathbb{A}})$. We then match the corresponding local orbital integrals for the unit elements of the spherical Hecke algebras; that is, we establish the Fundamental Lemma.
