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On the symmetry classes of functions

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Wuhan University Journal of Natural Sciences

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, 430072, Wuhan, Hubei, China

    Zhu Ping

  2. School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China

    Zhu Ping

  3. School of Mathematics and Statistics, Huazhong Normal University, 430079, Wuhan, Hubei, China

    Fan Yun

Authors
  1. Zhu Ping
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  2. Fan Yun
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Corresponding author

Correspondence to Zhu Ping.

Additional information

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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Ping, Z., Yun, F. On the symmetry classes of functions. Wuhan Univ. J. Nat. Sci. 10, 813–816 (2005). https://doi.org/10.1007/BF02832418

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  • DOI: https://doi.org/10.1007/BF02832418

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