摘要
Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several variables is a symmetry class, where ξi is any block character. Then we present a relationship among certain operators introduced for block character. Then we present a relationship among certain operators introduced for block characters. As a consequence, we obtain a decomposition of an arbitrary R-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.
Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several variables is a symmetry class, where ξi is any block character. Then we present a relationship among certain operators introduced for block character. Then we present a relationship among certain operators introduced for block characters. As a consequence, we obtain a decomposition of an arbitrary R-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.
作者
ZHU Ping~1,2, FAN Yun~3 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China
2. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
3. School of Mathematics and Statistics, Huazhong Normal University, Wuhan 430079, Hubei, China
基金
SupportedbytheNationalProgramonBasicScience(973Program,G1999075102)
