The action of the orthogonal group on planar vectors: invariants, covariants and syzygies

DOI10.1088/1751-8113/46/45/455202zbMath1285.22017OpenAlexW1996810379MaRDI QIDQ2866985

Boris I. Zhilinskiĭ, Guillaume Dhont

Publication date: 10 December 2013

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/14dcb891ea8c67ea00d75189962cba26f67f65d0

zbMATH Keywords

covariantsinvariantsorthogonal groupsyzygiesmolecular symmetryMolien function

Mathematics Subject Classification ID

Actions of groups and semigroups; invariant theory (associative rings and algebras) (16W22) Vector and tensor algebra, theory of invariants (15A72) Applications of Lie groups to the sciences; explicit representations (22E70) Actions of groups on commutative rings; invariant theory (13A50)

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A fast algorithm for the construction of integrity bases associated to symmetry-adapted polynomial representations: application to tetrahedral XY\(_{\mathrm{4}}\) molecules ⋮ Molien generating functions and integrity bases for the action of the \(\mathrm{SO}(3)\) and \(\mathrm{O}(3)\) groups on a set of vectors

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