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

TL;DR

This paper constructs a quotient ring related to diagonal coinvariants of complex reflection groups G(m,p,n) and determines its graded character, extending previous results from Coxeter groups using rational Cherednik algebra techniques.

Contribution

It generalizes Gordon's results for Coxeter groups to complex reflection groups G(m,p,n) by constructing a quotient ring and analyzing its graded character via category O of rational Cherednik algebras.

Findings

Constructed a quotient ring of diagonal coinvariants for G(m,p,n).

Determined the graded character of this quotient ring.

Extended known results from Coxeter groups to complex reflection groups.

Abstract

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 $\cO$ for the rational Cherednik algebra of $W$.