Realizations of the Irreducible Components of the Quasi-Regular Representation of Groups Transitive on Spheres. Invariant Subspaces

Abstract

Quasi-regular representations of groups transitive on spheres are investigated. An explicit description of the decomposition of the spherical harmonics into irreducible submodules under the action of these groups is given. Applications of these results to invariant subspaces are considered. The treatment differs from the existing books and is accessible to a wider audience as the use of Lie theory is minimal.