Noncommutative desingularization of orbit closures for some   representations of $GL_n$
  We describe noncommutative desingularizations of determinantal varieties, determinantal varieties defined by minors of generic symmetric matrices, and pfaffian varieties defined by pfaffians of generic anti-symmetric matrices. For maximal minors of square matrices and symmetric matrices, this gives a non-commutative crepant resolution. Along the way, we describe a method to calculate the quiver with relations for any non-commutative desingularizations coming from exceptional collections over partial flag varieties. 
Jerzy Weyman, Gufang Zhao
math.AG math.AC math.RT