Computing Wigner D-Matrices: Contradiction Found

[sale]

I am writing a program for computing the Wigner d-matrices and ran into an apparent contradiction:

Specifically computing d^1/2_{-1/2,1/2}

According to Edmonds, p.59, 4.1.27 this is given by

(-1)**[1/2-(-1/2)][1!/(1! 0!)]**{1/2} sin(b/2)=-sin(b/2)

Now for d^{1/2}_{1/2,-1/2}
From p.61, (4.4.1) we get -sqrt(1) d^0_{00} sin (b/2)=-sin(b/2)

However, from the relation d^j_{m'm}=(-1)**(m-m') d^j_{m,m'}

these two should have the same sign as (m-m')=1/2-(-1/2)=1 is odd

Could be it a typo in Edmonds?

 

[azntoon]

It is possible that there is a typo in Edmonds. However, it is also possible that the relation d^j_{m'm}=(-1)**(m-m') d^j_{m,m'} does not apply for the specific case you are considering. It may be worth double checking the equation and making sure that it is valid for the case you are looking at.