Theoretical review of group symmetries

How do you go and build in SU(2) into 3-d wavelet transform.

How do you build simple rotational symmetries, in 2-D for example (O(1), U(1)):

How should we engineer wavelets, and possibly modify the cascade in order to realize these symmetries.

How this would manifest itself, is that certain rotations and reflections, of an input image, would not generate changes in the coefficients.

Start in 2-d and extend to 3-d.