| On the Symmetry Classes of Functions |
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| 作者姓名： | ZHU Ping FAN Yun |
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| 作者单位： | [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 |
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| 基金项目： | Supported by the National Program on Basic Science （973 Program, G1999075102） |
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| 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.
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| 关 键 词： | 对称性 对称函数 线性代数 块幂等 |
| 文章编号： | 1007-1202（2005）05-0813-04 |
| 收稿时间： | 2004-09-03 |
On the symmetry classes of functions |
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| ZHU Ping FAN Yun.On the Symmetry Classes of Functions[J].Wuhan University Journal of Natural Sciences,2005,10(5):813-816. |
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| Authors: | Zhu Ping Fan Yun |
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| Institution: | (1) School of Mathematics and Statistics, Wuhan University, 430072 Wuhan, Hubei, China;(2) School of Science, Beijing University of Posts and Telecommunications, 100876 Beijing, China;(3) School of Mathematics and Statistics, Huazhong Normal University, 430079 Wuhan, Hubei, China |
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| Abstract: | 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.
Foundation item: Supported by the National Program on Basic Science (973 Program, G1999075102)
Biography: ZHU Ping(1974-), female, Ph. D., research direction: representation theory of finite groups. |
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| Keywords: | symmetry class strict symmetry class block character ξ i -symmetric function block idempotent |
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