A Converse Theorem for Split ${\mathrm{SO}}_{2l}$ over Finite Fields

Abstract

We prove a converse theorem for split even special orthogonal groups over finite fields. This is the only case left on converse theorems of split classical groups and the difficulty is the existence of the outer automorphism. In this paper, we develop new ideas and overcome this difficulty.

To appear in Acta Mathematica Sinica, English Series