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-valuedξi-symmetric functions of several v...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-valuedξi-symmetric functions of several variables is a symmetry class,whereξi 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.展开更多
基金Supported by the National Programon Basic Science(973 Program,G1999075102)
文摘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-valuedξi-symmetric functions of several variables is a symmetry class,whereξi 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.
