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

TL;DR

This paper investigates the structure of standard modules for the rational Cherednik algebra associated with the complex reflection group G(r,1,2), providing conditions for module morphisms and explicit formulas.

Contribution

It offers necessary and sufficient conditions for morphisms between standard modules and explicit formulas, advancing understanding of the algebra's representation theory.

Findings

Criteria for existence of module morphisms

Explicit formulas for morphisms

Enhanced understanding of G(r,1,2) representations

Abstract

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 $\Delta(\lambda)$ 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.