A contraction of SU(2) to the Heisenberg group
If a ball in two complex dimensions is subject to an appropriate one- parameter family of non-isotropic dilations, it tends to cover in the limit the Siegel domain defined by Im \(z_ 2> | z_ 1|^ 2\). If the boundary of the ball is identified with the special unitary group SU(2) and the boundary of the Siegel domain with the three-dimensional Heisenberg group H, this procedure induces a contraction of SU(2) to H. It is shown how this picture allows to realize the infinite-dimensional representations of H as limits of irreducibles of SU(2).
scientific article; zbMATH DE number 3944509