Full automorphism group of the generalized symplectic graph  

作　　者：ZENG LiWei CHAI Zhao FENG RongQuan MA ChangLi 

机构地区：[1]LMAM, School of Mathematical Sciences, Peking University [2]Science China Press [3]College of Mathematics and Information Science, Hebei Normal University

出　　处：《Science China Mathematics》2013年第7期1509-1520,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.10990011,11271004 and 61071221);the Doctoral Program of Higher Education of China(Grant No.20100001110007);the Natural Science Foundation of Hebei Province(Grant No.A2009000253)

摘　　要：Let Fq be a finite field of odd characteristic, m, v the integers with 1 ≤ m ≤ v and K a 2v × 2v nonsingular alternate matrix over Fq. In this paper, the generalized symplectic graph GSp2v（q, m） relative to K over Fq is introduced. It is the graph with m-dimensional totally isotropic subspaces of the 2v-dimensional symplectic space Fq（2v） as its vertices and two vertices P and Q are adjacent if and only if the rank of PKQw is 1 and the dimension of P ∩ Q is m - 1. It is proved that the full automorphism group of the graph GSp2v（q, m） is the projective semilinear symplectic group P∑p（2v, q）.Let Fq be a finite field of odd characteristic, m, ν the integers with 1≤m≤ν and Ka 2ν× 2ν nonsingular alternate matrix over Fq. In this paper, the generalized symplectic graph GSp2ν (q, m) relative to K over Fq is introduced. It is the graph with m-dimensional totally isotropic subspaces of the 2ν-dimensional symplectic space F(2ν)q as its vertices and two vertices P and Q are adjacent if and only if the rank of PKQT is 1 and the dimension of P ∩ Q is m-1. It is proved that the full automorphism group of the graph GSp2ν(q, m) is the projective semilinear symplectic group PΣp(2ν, q).

关 键 词：generalized symplectic graph AUTOMORPHISM projective generalized symplectic group totally isotropic subspace generalized dual polar graph 

分 类 号：O157.5[理学—数学]