Q: About the classification of infinite depth irreducible finite index maximal subfactors 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. 
