Modular decomposition numbers of cyclotomic Hecke and diagrammatic Cherednik algebras: a path theoretic approach

Cox, A. & Bowman, C. (2018). Modular decomposition numbers of cyclotomic Hecke and diagrammatic Cherednik algebras: a path theoretic approach. Forum of Mathematics, Sigma, doi: 10.1017/fms.2018.9

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Abstract

We introduce a path theoretic framework for understanding the representation theory of (quantum) symmetric and general linear groups and their higher-level generalizations over fields of arbitrary characteristic. Our first main result is a ‘super-strong linkage principle’ which provides degree-wise upper bounds for graded decomposition numbers (this is new even in the case of symmetric groups). Next, we generalize the notion of homomorphisms between Weyl/Specht modules which are ‘generically’ placed (within the associated alcove geometries) to cyclotomic Hecke and
diagrammatic Cherednik algebras. Finally, we provide evidence for a higher-level analogue of the classical Lusztig conjecture over fields of sufficiently large characteristic.

Publication Type: Article
Additional Information: © The Author(s) 2018. This is the accepted version of an an Open Access article to be distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. The Version of Record will be available online at: https://www.cambridge.org/core/journals/forum-of-mathematics-sigma
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/19977

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