Geodesic
Hilbert Ideals of Vector Invariants of s2 and S3
Journal of Lie theory, Tome 22 (2012) no. 4, pp. 1181-1196
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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 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.
Classification : 13P10, 13A50
Mots-clés : Hilbert ideals, vector invariants, symmetric groups 
@article{JLT_2012_22_4_JLT_2012_22_4_a13,
     author = {M. Sezer and \"O. \"Unl\"u},
     title = {Hilbert {Ideals} of {Vector} {Invariants} of s\protect\textsubscript{2} and {S\protect\textsubscript{3}}},
     journal = {Journal of Lie theory},
     pages = {1181--1196},
     year = {2012},
     volume = {22},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2012_22_4_JLT_2012_22_4_a13/}
}
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M. Sezer; Ö. Ünlü. Hilbert Ideals of Vector Invariants of s2 and S3. Journal of Lie theory, Tome 22 (2012) no. 4, pp. 1181-1196. http://geodesic.mathdoc.fr/item/JLT_2012_22_4_JLT_2012_22_4_a13/