表示论与数论讨论班——Theta correspondence and simple factors of global Arthur parameters

Abstract: 

Let $\pi$ be a cuspidal automorphic representation of a classical group or a metaplectic group. We show an exact relation between two invariants associated to $\pi$, one called the lowest occurrence index of $\pi$ which is an invariant arising from theta lifts and the other the location of the maximal positive pole of an Eisenstein series attached to $\pi$. As an application, we use this relation to show that certain global Arthur packets cannot contain cuspidal automorphic representations.