Analogs of Wigner-Eckart theorem for other groups

Question

Question: Are there analogs of the Wigner-Eckart theorem for continuous groups other than $SO(3)$?

Some motivation: In quantum mechanics, one often uses parity or Wigner-Eckart to evaluate the various integrals that arise in e.g. atomic transition amplitudes. If parity and rotational symmetry can be used to simplify integrals, it would surprise me if this were not true of other groups, too.

Answer 1

1. For compact groups see Theorem 2 on page 247 of

A. Barut, and R. Razka. Theory of Group Representations and Applications. Singapore, World Scientific Publishing, 1986.

2. For locally compact groups, see

A. U. Klimyk, Wigner–Eckart theorem for locally compact groups. Theor. Math. Phys. 8 (1971), p. 668–672.