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.
1
Dept. of Mathematics, Bilkent University, Ankara 06800, Turkey
Müfit Sezer; Özgün 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/JOLT_2012_22_4_a13/
@article{JOLT_2012_22_4_a13,
author = {M\"ufit Sezer and \"Ozg\"un \"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/JOLT_2012_22_4_a13/}
}
TY - JOUR
AU - Müfit Sezer
AU - Özgün Ünlü
TI - Hilbert Ideals of Vector Invariants of s2 and S3
JO - Journal of Lie Theory
PY - 2012
SP - 1181
EP - 1196
VL - 22
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2012_22_4_a13/
ID - JOLT_2012_22_4_a13
ER -
%0 Journal Article
%A Müfit Sezer
%A Özgün Ünlü
%T Hilbert Ideals of Vector Invariants of s2 and S3
%J Journal of Lie Theory
%D 2012
%P 1181-1196
%V 22
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2012_22_4_a13/
%F JOLT_2012_22_4_a13
