局部环上典型群BN-对构造

Construction of BN-pairs of classical groups over local rings

构造群的BN-对是Building理论中的一个重要课题.由于每个BN-对都对应一个Weyl群,通过研究Weyl群可以得到群的各种性质,从而BN-对成为研究群的一个重要工具.假定R是一个局部环,通过采用矩阵方法构造了R上一般线性群、辛群、正交群的BN-对.构造了局部环上一族具有包含关系的一般线性群的BN-对,并且证明了这组一般线性群和对应的BN-对之间满足一个交换图.

The construction of BN-pairs of groups is an important topic in Building theory.Since every BN-pair of a group corresponds to a group of Weyl type,the properties of the group are obtained by discussing the group of Weyl type.Therefore,BN-pair is a useful tool in studying groups.Let R be a local ring.Using matrix method,BN-pairs of the general linear group,orthogonal group and symplectic group over local ring Rare constructed,respectively.Furthermore,BN-pairs of a family of general linear groups over local ring Rare also discussed,and these general linear groups and their corresponding BN-pairs satisfy a communicative diagram of groups.