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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The authors would like to thank Joe Chuang, Anton Cox, Kai Meng Tan, and Ben Webster for helpful conversations during the preparation of this manuscript. We also thank the referee for helpful comments. The authors are grateful for the financial support received from the Royal Commission for the Exhibition of 1851, the London Mathematical Society, and the Japan Society for the Promotion of Science.
© 2017 American Mathematical Society.