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arXiv · 1706.07128

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

C. Bowman·A. G. Cox
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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 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.

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BibTeXRIS

C. Bowman, A. G. Cox. 2017-06-21. Modular decomposition numbers of cyclotomic Hecke and diagrammatic Cherednik algebras: A path theoretic approach. https://arxiv.org/abs/1706.07128

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