Blocks of restricted rational Cherednik algebras for $G(m,d,n)$

TL;DR

This paper investigates the structure of blocks in restricted rational Cherednik algebras associated with wreath product groups, using Dunkl-Opdam subalgebras at a specific parameter value.

Contribution

It provides a detailed description of the block decomposition for these algebras, enhancing understanding of their representation theory.

Findings

Block decomposition characterized for $G(m,d,n)$

Connection established with Dunkl-Opdam subalgebras at $t=0$

New insights into the structure of restricted rational Cherednik algebras

Abstract

We study the Dunkl-Opdam subalgebra of the rational Cherednik algebra for wreath products at $t=0$, and use this to describe the block decomposition of restricted rational Cherednik algebras for $G(m,d,n)$.