Clebsch Gordan coefficients

[LagrangeEuler]

In CG coefficients methodology there is convention
$$\langle J_1 J_2 J_1 J-J_1|J_1 J_2 J J \rangle \geq 0$$
So if we have $J_1=1$, $J_2=1/2$
$$\langle 1 \quad 1/2 \quad 1/2 \quad 1|1 \quad 1/2 \quad 3/2 \quad 3/2\rangle \geq 0$$
using this convention. However, because $J=3/2$ is maximal value of angular moment, this is only CG coefficient and we could write
$$\langle 1 \quad 1/2 \quad1/2 \quad 1|1 \quad 1/2 \quad 3/2 \quad 3/2\rangle =1$$
Now if we work with $J_-$ operator we will obtain that
$$\langle 1 \quad 1/2 \quad -1/2 \quad -1|1 \quad 1/2 \quad -3/2 \quad -3/2\rangle =1$$
Do we have some similar convention for this lowest value of angular momentum?

 

[blue_leaf77]

Do we have some similar convention for this lowest value of angular momentum?

You can verify it by looking at Clebsch-Gordan coefficients table, e.g. https://i.ytimg.com/vi/rVdumZRqDs8/maxresdefault.jpg.