You can find quiver and relations (not sure if they are admissible always) here: http://www.math.uni-bonn.de/ag/stroppel/Quivers.pdf In particular the explicit algebra is only fully understoof for $sl_4$ and below.

You can find quiver and relations (not sure if they are admissible always) here: http://www.math.uni-bonn.de/ag/stroppel/Quivers.pdf In particular the explicit algebra is only fully understoof for $sl_4$ and below. See also https://link.springer.com/article/10.1007/s00222-006-0005-2 which gives results on the calculation on the quiver and relations for those blocks. It is an open question whether the field coefficients can always be choosen to be +1 or -1, see the end of this article.