Unitary representations of three dimensional Lie groups revisited: An approach via harmonic functions

Abstract

Harmonic functions of the three dimensional Lie groups defined on certain manifolds related to the Lie groups themselves and carrying all their unitary representations are explicitly constructed. The realisations of these Lie groups are shown to be related with each other by either natural operations as real forms or Inönü-Wigner contractions.

The title was changed; More details are given for the constuction of harmonic functions 19 pages

References in corpus (2)

• Spherical harmonics and integration in superspace
• Landau quantum systems: an approach based on symmetry

Cited by in corpus (2)

• An overview of generalised Kac-Moody algebras on compact real manifolds
• Infinite degeneracy of Landau levels from the Euclidean symmetry with central extension revisited