Blocks of category $\mathcal{O}$ for rational Cherednik algebras and of cyclotomic Hecke algebras of type G(r,p,n)

TL;DR

This paper classifies the blocks of category O for rational Cherednik algebras and cyclotomic Hecke algebras of type G(r,p,n) using residue equivalence of multi-partitions, advancing understanding of their algebraic structures.

Contribution

It introduces a classification method for blocks of these algebras based on residue equivalence, providing a new combinatorial approach.

Findings

Classification of blocks for rational Cherednik algebras achieved.

Classification of blocks for cyclotomic Hecke algebras achieved.

Residue equivalence effectively distinguishes blocks.

Abstract

We classify blocks of category $\mathcal{O}$ for rational Cherednik algebras and of cyclotomic Hecke algebras of type G(r,p,n) by using the "residue equivalence" for multi-partitions.