This is a preview of subscription content, log in via an institution to check access.
References
E. Bierstone, Lifting isotopies from orbit spaces, Topology 14 (1975), 245–252.
E. Bierstone, General position of equivariant maps, Trans. Amer. Math. Soc. 234 (1977), 447–466.
N. Bourbaki, Groupes et algèbres de Lie, Chap. 4–6, Hermann, Paris, 1968.
P. Chossat, Solutions avec symétry diédrale dans les problèmes de bifurcation invariants par symétry sphérique, C. R. A. S., Série I, 297 (1983), 639–642.
J. Dieudonné, Foundations of Modern Analysis, Academic Press, New York and London, 1967.
M. J. Field, Stratifications of equivariant varieties, Bull. Austral. Math. Soc. 16 (1977), 279–295.
M. J. Field, Transversality in G-manifolds, Trans. Amer. Math. Soc. 231 (1977), 429–450.
M. J. Field, Equivariant bifurcation theory and symmetry breaking, preprint, University of Sydney (1988).
C. Gibson, K. Wirthmüller, A. A. du Plessis & E. Looijenga, Topological stability of smooth mappings, Springer Lecture Notes in Math. 553 (1976).
M. Golubitsky, The Bénard problem, symmetry and the lattice of isotropy subgroups, in Bifurcation Theory, Mechanics and Physics, C. P. Bruter et al. eds. D. Riedel, Dordrecht-Boston-Lancaster (1983), 225–257.
M. Golubitsky & D. G. Schaeffer, Bifurcations with O(3) symmetry including applications to the Bénard problem, Commun. Pure and Applied Math. 35 (1982), 81–111.
M. Golubitsky & D. G. Schaeffer, Singularities and Groups in Bifurcation Theory, Vol. I, Applied Math. Sciences 51, Springer-Verlag, New York (1985).
M. Golubitsky, D. G. Schaeffer & I. Stewart, Singularities and Groups in Bifurcation Theory, Vol. II, Applied Math. Sciences 69, Springer-Verlag, New York (1988).
S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York (1962).
S. Helgason, Differential Geometry. Lie Groups and Symmetric Spaces, Academic Press, New York-San Francisco-London, (1978).
H. Hironaka, Subanalytic sets, in Number Theory, Algebraic Geometry and Commutative Algebra, Volume in honour of Y. Akizuki, Kinokumiya, Tokyo, (1973), 453–493.
R. Lauterbach, An example of symmetry breaking with submaximal isotropy subgroup, Contemporary Math. 56 (1986), 217–222.
D. Luna, Slices étales, Bull. Math. Soc. Grancs, Mémoire 33 (1973), 81–105.
J. Mather, Stratifications and mappings, in Proceeding of the Dynamical Systems Conference, Salvador, Brazil, ed. M. Peixoto, Academic Press, New York-San Franscisco-London, (1973).
P. Orlik, L. Solomon & H. Terao, On Coxeter arrangements and the Coxeter number, to appear.
W. Pawlucki, Quasi-regular boundary and Stokes' formula for a sub-analytic leaf, Springer Lecture Notes in Mathematics 1165 (1985), 235–252.
V. Poenaru, Singularités C∞ en présence de symétrie, Springer Lecture Notes in Math. 510 (1976).
G. W. Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975), 64–68.
G. W. Schwarz, Lifting smooth homotopies of orbit spaces, Publ. Math. I.H.E.S. 51 (1980), 37–134.
J. C. Tougeron, Idéaux de fonctions différentiables, Springer-Verlag, New York-Berlin, (1972).
G. Warner, Harmonic analysis on Semi-simple Lie Groups, Springer-Verlag, Berlin, Heidelberg, New York, (1972).
Author information
Authors and Affiliations
Additional information
Communicated by M. Golubitsky
Rights and permissions
About this article
Cite this article
Field, M.J., Richardson, R.W. Symmetry breaking and the maximal isotropy subgroup conjecture for reflection groups. Arch. Rational Mech. Anal. 105, 61–94 (1989). https://doi.org/10.1007/BF00251598
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00251598