Four Dimensional Orbit Spaces of Compact Coregular Linear Groups

Determination of the orbit spaces of non - coregular compact linear groups with one relation among the basic polynomial invariants in the P̂ - matrix approach ∗

Co-regular Spaces and Genus One Curves

Some examples of coregular spaces were mentioned last time binary quadratic forms, binary cubic forms etc. Clearly, any pre-homogeneous space is a vector space. Coregular spaces were first classified by Littelman (1989) for semisimple irreducible representations; there are around 50 of them including infinite families. A lot of these spaces come from Vinberg theory, something that’ll be discuss...

ar X iv : h ep - t h / 95 10 16 2 v 1 2 3 O ct 1 99 5 Orbit spaces of reflection groups with 2 , 3 and 4 basic polynomial invariants ∗

Functions which are covariant or invariant under the transformations of a compact linear group can be advantageously expressed in terms of functions defined in the orbit space of the group, i.e. as functions of a finite set of basic invariant polynomials. The equalities and inequalities defining the orbit spaces of all finite coregular real linear groups (most of which are crystallographic grou...

The Orbit Space Approach to the Theory of Phase Transitions: The Non-Coregular Case

We consider the problem of the determination of the isotropy classes of the orbit spaces of all the real linear groups, with three independent basic invariants satisfying only one independent relation. The results are obtained in the P̂ -matrix approach solving a universal differential equation (master equation) which involves as free parameters only the degrees da of the invariants. We begin wi...

Orbit Spaces Arising from Isometric Actions on Hyperbolic Spaces

Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology.  Dimension of is called the cohomogeneity of the action of  on . If is a differentiable manifold  of  cohomogeneity one under the action of  a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...