An analogue of row removal for diagrammatic Cherednik algebras

TL;DR

This paper establishes a row removal analogue for diagrammatic Cherednik algebras, providing new insights into their graded decomposition numbers and extension groups, especially over fields of arbitrary characteristic.

Contribution

It introduces a novel row removal theorem for diagrammatic Cherednik algebras, advancing understanding of their graded decomposition numbers and extension groups.

Findings

Proves a row removal theorem for diagrammatic Cherednik algebras.

Provides a reduction theorem for graded decomposition numbers.

Extends results to fields of arbitrary characteristic.

Abstract

We prove an analogue of James-Donkin row removal theorems for arbitrary diagrammatic Cherednik algebras. This is one of the first results concerning the (graded) decomposition numbers of these algebras over fields of arbitrary characteristic. As a special case, our results yield a new reduction theorem for graded decomposition numbers and extension groups for cyclotomic q-Schur algebras.