Symmetry breaking and the maximal isotropy subgroup conjecture for reflection groups

DOI10.1007/BF00251598zbMath0824.58017OpenAlexW2093584183WikidataQ122911201 ScholiaQ122911201MaRDI QIDQ1813209

Michael Field, R. W. jun. Richardson

Publication date: 25 June 1992

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00251598

zbMATH Keywords

transversalitysymmetry breakingbifurcation theoryreflection groupsmaximal isotropy

Mathematics Subject Classification ID

Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25) Local and nonlocal bifurcation theory for dynamical systems (37G99) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

Related Items (21)

Critical sections of gauge functionals: A symmetry approach ⋮ A splitting lemma for equivariant dynamics ⋮ The dynamics of \(n\) weakly coupled identical oscillators ⋮ Counting symmetry-breaking solutions to symmetric variational problems ⋮ Semi-invariants, equivariants and algorithms ⋮ Symmetry breaking in equivariant bifurcation problems ⋮ Computational methods for bifurcation problems with symmetries - with special attention to steady state and Hopf bifurcation points ⋮ Breaking Indecision in Multiagent, Multioption Dynamics ⋮ Equivariant bifurcation theory and symmetry breaking ⋮ Symmetry-breaking and branching patterns in equivariant bifurcation theory. I ⋮ Spontaneous symmetry breaking in higher dimensional fixed point spaces ⋮ Symmetry breaking and branching patterns in equivariant bifurcation theory. II ⋮ Bifurcation and symmetry breaking ⋮ Intermittency as a codimension-three phenomenon ⋮ Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry ⋮ A CAUTIONARY TALE OF COUPLING CELLS WITH INTERNAL SYMMETRIES ⋮ Steady-state bifurcation with O(3)-symmetry ⋮ On the zero set of G-equivariant maps ⋮ Michel theory of symmetry breaking and gauge theories ⋮ Breaking of permutation symmetry and diagonal group action: Nielsen model and the standard model as low-energy limit ⋮ Equivariant bifurcation, quadratic equivariants, and symmetry breaking for the standard representation of S _k

Cites Work

• Singularities and groups in bifurcation theory. Volume I
• Lifting smooth homotopies of orbit spaces
• Smooth functions invariant under the action of a compact Lie group
• Lifting isotopies from orbit spaces
• Bifurcations withO(3) symmetry including applications to the Bénard problem
• General Position of Equivariant Maps
• Transversality in G-Manifolds
• Stratifications of equivariant varieties
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