On the symmetry classes of functions
Zhu Ping, Fan Yun · Wuhan University Journal of Natural Sciences · 2005
LetR 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 theR-valuedξ i -symmetric functions of several variables is a symmetry class, whereξ i 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 arbitraryR-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.