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

Abstract

We introduce a path-theoretic framework for understanding the representation theory of (quantum) symmetric and general linear groups and their higher level generalisations 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 generalise 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.

38 pages, 9 figures

References in corpus (6)

• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Blocks of cyclotomic Hecke algebras
• The many graded cellular bases of Hecke algebras
• Generalised column removal for graded homomorphisms between Specht modules
• Characteristic-free bases and BGG resolutions of unitary simple modules for quiver Hecke and Cherednik algebras

Cited by in corpus (2)

• The many graded cellular bases of Hecke algebras
• Characteristic-free bases and BGG resolutions of unitary simple modules for quiver Hecke and Cherednik algebras