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Molien functions and generalized integrity bases for SO(3) and related groups

Abstract : The goal is to show how to obtain Molien functions for SO(3) invariant and covariant modules, how to recast them in an appropriate form when these modules are not free, and how to use them to build integrity bases for free modules or their generalization in the case of non-free covariants modules. We also explain how to easily derive O(3) invariants and covariants basis from SO(3) ones. However, applications of SO(3) invariant and covariant bases extends to cases such as the modelling of potential energy or dipole moment hypersurfaces in quantum chemistry, where O(3)-symmetry is expected to hold, unless parity violation is considered, but where the use of the SO(3) invariant ring is more practical than that of O(3).
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01222972
Contributor : Patrick Cassam-Chenaï <>
Submitted on : Thursday, January 7, 2021 - 5:40:00 PM
Last modification on : Tuesday, January 12, 2021 - 10:37:44 AM

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cov-SO3_v02.pdf
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  • HAL Id : hal-01222972, version 2
  • ARXIV : 1511.01311

Citation

Guillaume Dhont, Patrick Cassam-Chenaï, Frédéric Patras. Molien functions and generalized integrity bases for SO(3) and related groups. 2021. ⟨hal-01222972v2⟩

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