Theta correspondence and simple factors in global Arthur parameters

TL;DR

This paper establishes bounds on certain factors of global Arthur parameters for automorphic representations using theta correspondence and L-function poles, with refined results for generic packets.

Contribution

It provides new bounds on $( ext{chi},b)$-factors of global Arthur parameters for automorphic representations of classical and metaplectic groups, utilizing theta correspondence techniques.

Findings

Bound on $b$ for $( ext{chi},b)$-factors established.

More precise relations derived for generic global $A$-packets.

Results connect poles of $L$-functions with Arthur parameters.

Abstract

By using results on poles of $L$-functions and theta correspondence, we give a bound on $b$ for $(\chi,b)$-factors of the global Arthur parameter of a cuspidal automorphic representation $\pi$ of a classical group or a metaplectic group where $\chi$ is a conjugate self-dual automorphic character and $b$ is an integer which is the dimension of an irreducible representation of $\mathrm{SL}_{2}(\mathbf{CC})$. We derive a more precise relation when $\pi$ lies in a generic global $A$-packet.