  We completely characterize perfect, permutative, irreducible representations
of an ultragraph Leavitt path algebra. For this we extend to ultragraph Leavitt
path algebras Chen's construction of irreducible representations of Leavitt
path algebras. We show that these representations can be built from branching
system and characterize irreducible representations associated to perfect
branching systems. Along the way we improve the characterization of
faithfulness of Chen's irreducible representations.
