Modular Decomposition Numbers of Cyclotomic Hecke and Diagrammatic Cherednik Algebras: a Path Theoretic Approach

Bowman, Christopher, Cox, A.G. (2018) Modular Decomposition Numbers of Cyclotomic Hecke and Diagrammatic Cherednik Algebras: a Path Theoretic Approach. Forum of Mathematics, Sigma, 6 . ISSN 2050-5094. (doi:10.1017/fms.2018.9) (KAR id:67588)

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.

Item Type: Article 10.1017/fms.2018.9 Q ScienceQ Science > QA Mathematics (inc Computing science)Q Science > QA Mathematics (inc Computing science) > QA150 Algebra Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Christopher Bowman 11 Jul 2018 08:46 UTC 16 Feb 2021 13:56 UTC https://kar.kent.ac.uk/id/eprint/67588 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-6046-8930