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arXiv · 2207.04495

Syzygies for the vector invariants of the dihedral group

M. Domokos
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Abstract

The problem of finding generators of the $GL$-ideal of the relations between the generators of the algebra of invariants of the dihedral group acting on $m$-tuples of vectors from its defining $2$-dimensional representation is studied. It is shown that this $GL$-ideal is generated by relations depending on no more than $3$ vector variables. A minimal $GL$-ideal generating system is found for the case when $m=2$, and for the case of the dihedral group of order $8$ and arbitrary $m$.

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M. Domokos. 2022-07-10. Syzygies for the vector invariants of the dihedral group. https://arxiv.org/abs/2207.04495

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