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We show that for the family of complex reflection groups $G=G(m,p,2)$appearing in the Shephard--Todd classification, the endomorphism ring of thereduced hyperplane arrangement $A(G)$ is a non-commutative resolution for thecoordinate ring of the discriminant $\Delta$ of $G$. This furthers the work ofBuchweitz, Faber and Ingalls who showed that this result holds for any truereflection group. In particular, we construct a matrix factorization for$\Delta$ from $A(G)$ and decompose it using data from the irreduciblerepresentations of $G$. For $G(m,p,2)$ we give a full decomposition of thismatrix factorization, including for each irreducible representation acorresponding a maximal Cohen--Macaulay module. The decomposition concludesthat the endomorphism ring of the reduced hyperplane arrangement $A(G)$ will bea non-commutative resolution.

Non-commutative resolutions for the discriminant of the complex reflection group $G(m,p,2)$