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      Hilbert ideals of vector invariants of s2 and S3

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      Author
      Sezer, M.
      Ünlü, Ö.
      Date
      2012
      Source Title
      Journal of Lie Theory
      Print ISSN
      0949-5932
      Publisher
      Heldermann Verlag
      Volume
      22
      Issue
      4
      Pages
      1181 - 1196
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      The Hilbert ideal is the ideal generated by positive degree invariants of a finite group. We consider the vector invariants of the natural action of S n . For S 2 we compute the reduced and universal Gröbner bases for the Hilbert ideal. As well, we identify all initial form ideals of the Hilbert ideal and describe its Gröbner fan. In modular characteristics, we show that the Hilbert ideal for S 3 can be generated by polynomials of degree at most three and the reduced Gröbner basis contains no polynomials that involve variables from four or more copies. Our results give support for conjectures for improved degree bounds and regularity conditions on the Gröbner bases for the Hilbert ideal of vector invariants of S n. © 2012 Heldermann Verlag.
      Keywords
      13P10
      13A50
      Permalink
      http://hdl.handle.net/11693/21428
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