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TitleHilbert ideals of vector invariants of $S_2$ and $S_3$.
Author(s) "Ozgün "Unlü, Müfit Sezer
TypeArticle in Journal
AbstractThe Hilbert ideal is the ideal generated by positive degree invariants of a finite group. We consider the vector invariants of the natural action of Sn. For S2 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 S3 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 Sn.
KeywordsHilbert ideals, vector invariants, symmetric groups.
ISSN0949-5932
URL http://www.heldermann.de/JLT/JLT22/JLT224/jlt22054.htm
LanguageEnglish
JournalJ. Lie Theory
Volume22
Number4
Pages1181--1196
PublisherHeldermann, Lemgo
Year2012
Edition0
Translation No
Refereed No
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