A Converse Theorem for Split SO_(2l) over Finite Fields  

作　　者：Alexander HAZELTINE Bai Ying LIU 

机构地区：[1]Department of Mathematics,Purdue University,150 N.University St.,West Lafayette,IN 47907,USA E-mail:[e-mail] [e-mail]

出　　处：《Acta Mathematica Sinica,English Series》2024年第3期731-771,共41页数学学报（英文版）

基　　金：partially supported by the NSF Grants DMS-1848058;partially supported by the NSF Grants DMS-1702218, DMS-1848058;start-up funds from the Department of Mathematics at Purdue University.

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

关 键 词：Converse theorems generic cuspidal representations even special orthogonal groups 

分 类 号：O152[理学—数学]