Geodesic
Hilbert Ideals of Vector Invariants of s2 and S3
Journal of Lie theory, Tome 22 (2012) no. 4, pp. 1181-1196

Voir la notice de l'article provenant de la source Heldermann Verlag

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 Gr�bner bases for the Hilbert ideal. As well, we identify all initial form ideals of the Hilbert ideal and describe its Gr�bner 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 Gr�bner 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 Gr�bner bases for the Hilbert ideal of vector invariants of Sn.
Classification : 13P10, 13A50
Mots-clés : Hilbert ideals, vector invariants, symmetric groups 
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     author = {M. Sezer and �. �nl� },
     title = {Hilbert {Ideals} of {Vector} {Invariants} of s\protect\textsubscript{2} and {S\protect\textsubscript{3}}},
     journal = {Journal of Lie theory},
     pages = {1181--1196},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JLT_2012_22_4_JLT_2012_22_4_a13/}
}
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M. Sezer; �. �nl� . 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/