The Langlands functoriality conjecture is one of the far-reaching conjectures of the Langlands program.
Over number fields, Cogdell, Kim, Piatetski-Shapiro, and Shahidi prove this conjecture for globally generic cuspidal automorphic representations from the split classical groups, unitary groups or quasi-split special orthogonal groups to the general linear groups. Lomelí extends this result to split classical groups and unitary groups in positive characteristics.
In this talk, we are going to study Langlands functoriality conjecture for globally generic cuspidal automorphic representations of quasi-split non-split even special orthogonal groups in positive characteristics by means of the converse theorem combine with the Langlands-Shahidi method.