Kleshchev's decomposition numbers for diagrammatic Cherednik algebras
arXiv:1507.06631 · doi:10.1090/tran/7054
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.
32 pages, v2 has minor corrections and some new, larger examples, v3 is the final version, to appear in Trans. Amer. Math. Soc. and includes a new section with a detailed proof of our decomposition theorem