Orbit spaces of compact coregular simple Lie groups with 2, 3 and 4 basic polynomial invariants: Effective tools in the analysis of invariant potentials

DOI10.1063/1.532294zbMath1001.22019OpenAlexW2088311584WikidataQ115328850 ScholiaQ115328850MaRDI QIDQ4260568

G. Sartori, Vittorino Talamini

Publication date: 16 December 2002

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

Full work available at URL: https://doi.org/10.1063/1.532294

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Related Items (6)

Lie-Poincaré transformations and a reduction criterion in Landau theory ⋮ Constructive axiomatic approach to the determination of the orbit spaces of coregular compact linear groups ⋮ A fast algorithm for the construction of integrity bases associated to symmetry-adapted polynomial representations: application to tetrahedral XY\(_{\mathrm{4}}\) molecules ⋮ Geometric invariant theory approach to the determination of ground states of D-wave condensates in isotropic space ⋮ Molien generating functions and integrity bases for the action of the \(\mathrm{SO}(3)\) and \(\mathrm{O}(3)\) groups on a set of vectors ⋮ Flat bases of invariant polynomials and P̂-matrices of E7 and E8

Cites Work

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• The geometry of spontaneous symmetry breaking
• Inequalities defining orbit spaces
• Consequences of the complex character of the internal symmetry in supersymmetric theories
• Representations and representative functions of Lie groups. III
• Universality in orbit spaces of compact linear groups
• Smooth functions invariant under the action of a compact Lie group
• Representations of simple Lie groups with regular rings of invariants
• A theorem on orbit structures (strata) of compact linear Lie groups
• Symmetry breaking patterns and extended Morse theory
• Hilbert's Fourteenth Problem
• Extended integrity bases of finite groups
• Orbit spaces of reflection groups with 2, 3 and 4 basic polynomial invariants
• S Theorem and Construction of the Invariants of the Semisimple Compact Lie Algebras
• Classification of Irreducible Unitary Representations of Compact Simple Lie Groups. I
• Classification of Irreducible Unitary Representations of Compact Simple Lie Groups. II
• Invariants of Finite Groups Generated by Reflections

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