Kleshchev's decomposition numbers for diagrammatic Cherednik algebras
Christopher Bowman, Liron Speyer

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.
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