Unitary representations of three dimensional Lie groups revisited: A short tutorial via harmonic functions.

The representation theory of three dimensional real and complex Lie groups is reviewed from the perspective of harmonic functions defined over certain appropriate manifolds. An explicit construction of all unitary representations is given. The realisations obtained are shown to be related with each other by either natural operations as real forms or Inönü–Wigner contractions. [ABSTRACT FROM AUTHOR]