The orthogonal group action on spatial vectors: invariants, covariants, and syzygies

Abstract : The present paper on the SO(3) invariants and covariants built from N vectors of the three–dimensional space is the follow-up of our previous article [1] dealing with planar vectors and SO(2) symmetry. The goal is to propose integrity basis for the set of SO(3) invariants and covariant free modules and easy-to-use generating families in the case of non-free covariants modules. The existence of such non-free modules is one of the noteworthy features unseen when dealing with finite point groups, that we want to point out. As in paper [1], the Molien function plays a central role in the conception of these bases. The Molien functions are computed and checked by the use of two independent paths. The first computation relies on the Molien integral [2] and requires the matrix representation of the group action on the N spatial vectors. The second path considers the Molien function for only one spatial vector as the elementary building material from which are worked out the other Molien functions.
Type de document :
Pré-publication, Document de travail
Contributeur : Patrick Cassam-Chenaï <>
Soumis le : samedi 31 octobre 2015 - 17:13:37
Dernière modification le : mercredi 13 avril 2016 - 10:44:02


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  • HAL Id : hal-01222972, version 1
  • ARXIV : 1511.01311



Guillaume Dhont, Patrick Cassam-Chenaï, Boris Zhilinskii, Frédéric Patras. The orthogonal group action on spatial vectors: invariants, covariants, and syzygies. 2015. <hal-01222972>



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