Irreducible representations of the $C\sp{\ast}$-algebra generated by an $n$-normal operator

For $A$ an $n$-normal operator on Hilbert space, we determine the irreducible representations of ${C^ \ast }(A)$, the ${C^ \ast }$-algebra generated by $A$ and the identity. For $A$ a binormal operator, we determine an explicit description of the topology on the space of unitary equivalence classes of irreducible representations of ${C^ \ast }(A)$.