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

  • Valery V. VolchkovEmail author
  • Vitaly V. Volchkov
Part of the Springer Monographs in Mathematics book series (SMM)


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.


Spherical Harmonic Irreducible Component Invariant Subspace Linear Span Isotropy Subgroup 
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Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  1. 1.Mathematical DepartmentDonetsk National UniversityDonetskUkraine

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