Theta correspondence and simple factors in global 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 ${\mathrm{SL}<!--FUNCTION\; APPLICATION-->}_2(ℂ)$. We derive a more precise relation when $\pi$ lies in a generic global $A$-packet.