yψ ց m//G a/WV → t /WG where a ⊆ t is a subspace, WV ⊆ GL(a ) is a reflection group, and ψ is faithfully flat with irreducible generic fibers. Note that WV being a reflection group implies that a /WV is isomorphic to an affine space. The group WV is a very subtle invariant of V which plays a similar role as the Weyl group of the restricted root system for a symmetric space. The morphism ψ facto...

in this paper we introduce the concept of generalized baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. we give some inequalities for the generalized baer-invariant of a pair of finite groups, when ? is considered to be the schur-baer variety. further, we present a sufficient condition under which the order of the generalized baer-invariant of a pair of finite ...

We consider the problem of designing adapted kernels for approximating functions invariant under a known finite group action. We introduce the class of argumentwise invariant kernels, and show that they characterize centered square-integrable random fields with invariant paths, as well as Reproducing Kernel Hilbert Spaces of invariant functions. Two subclasses of argumentwise kernels are consid...