Parity rule for wigner D-matrices

[tommyli]

Hi!

Does anyone know how Wigner D-matrices transform under parity?

Is it something like
$$D^j_{m m'} (\pi - \theta, \phi + \pi) = (-1)^{j +m-m'} D^j_{m m'}(\theta, \phi)$$?

 

[read]

Probably for j=(2n+1)/2 this is not defined because half-integer spin operator does not commute with the parity operator.