Kleshchev's decomposition numbers for diagrammatic Cherednik algebras

TL;DR

This paper develops graded isomorphisms for diagrammatic Cherednik algebras, revealing new structural insights and enabling the first results on their graded decomposition numbers over arbitrary fields.

Contribution

It introduces a family of graded isomorphisms that connect subquotients of diagrammatic Cherednik algebras, advancing understanding of their structure and decomposition numbers.

Findings

Established graded isomorphisms between algebra subquotients

Derived new structural information for classical q-Schur algebras

Proved initial results on graded decomposition numbers in arbitrary characteristic

Abstract

We construct a family of graded isomorphisms between certain subquotients of diagrammatic Cherednik algebras as the quantum characteristic, multicharge, level, degree, and weighting are allowed to vary; this provides new structural information even in the case of the classical q-Schur algebra. This also allows us to prove some of the first results concerning the (graded) decomposition numbers of these algebras over fields of arbitrary characteristic.