MathOverflow Asked by Mare on August 1, 2020

In Vybornov – Perverse sheaves, Koszul IC-modules, and the quiver for the category $mathscr O$ an algorithm is presented to calculate quiver and relations for blocks of category $mathcal{O}$ .

Question 1: Is this algorithm implemented in practise already? Can one obtain quiver and relations in some program and obtain those quiver and relations in the GAP-package QPA?

How effective/fast is this algorithm? Can one expect to obtain quiver and relations also for the $E_n$ types? Maybe there is now also a better approach in the meantime since the article is from 2007.

Question 2: The article ends with the quesiton whether the relations can be always choosen such that they contain only the field elements $0$, $-1$ or 1. Has this question been answered?

In http://ems.math.uni-bonn.de/ag/stroppel/Quivers.pdf , one can find quiver and relations for types $A_2 , B_2 , G_2$ and $A_3$.

Question 3: Can one also find quiver and relations for type $B_3$ and $C_3$ in the literature?

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