Rational Cherednik algebras and diagonal coinvariants of G(m,p,n)

We construct a quotient ring of the ring of diagonal coinvariants of the complex reflection group $W=G(m,p,n)$ and determine its graded character. This generalises a result of Gordon for Coxeter groups. The proof uses a study of category $\text{cO}$ for the rational Cherednik algebra of $W$.