Singular polynomials for the rational Cherednik algebra for G(r,1,2)

We study the rational Cherednik algebra attached to the complex reflection group $G(r,1,2)$. Each irreducible representation $S^{\lambda }$ of $G(r,1,2)$ corresponds to a standard module $\mathrm{\Delta }(\lambda )$ for the rational Cherednik algebra. We give necessary and sufficient conditions for the existence of morphism between two of these modules and explicit formulas for them when they exist.