The Temperley Lieb subfactors $A_{\infty}$ are the first examples of infinite depth irreducible finite index maximal subfactors. We can see these subfactors as coming from the simple Lie group $SU(2)$.

I first asked here if there exists others infinite depth irreducible finite index maximal subfactors.

Noah Snyder answered "yes" by giving others examples coming from $SU(3)$.

**Question:** What's the classification of all the infinite depth irreducible finite index maximal subfactors coming from the simple Lie groups ?

Bonus open problem: is there exist such a subfactor **not** coming from a group.