On the contraction of so(4) to iso(3)

TL;DR

This paper demonstrates how certain finite-dimensional representations of so(4) can be contracted to infinite-dimensional representations of iso(3), revealing a connection between these algebraic structures.

Contribution

It constructs explicit sequences of finite-dimensional so(4) representations that contract to any given irreducible representation of iso(3).

Findings

Finite-dimensional so(4) representations can be contracted to infinite-dimensional iso(3) representations.

The contraction process is explicitly constructed for irreducible representations.

The work bridges the representation theories of so(4) and iso(3).

Abstract

For any skew-Hermitian integrable irreducible infinite dimensional representation $\eta$ of $iso(3)$, we find a sequence of (finite dimensional) irreducible representations $\rho_n$ of $so(4)$ which contract to $\eta$.