Kleshchev's decomposition numbers for diagrammatic Cherednik algebras
Representation Theory
2018-02-20 v3
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.
Keywords
Cite
@article{arxiv.1507.06631,
title = {Kleshchev's decomposition numbers for diagrammatic Cherednik algebras},
author = {Christopher Bowman and Liron Speyer},
journal= {arXiv preprint arXiv:1507.06631},
year = {2018}
}
Comments
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