Bowman-Scargill, Chris orcid.org/0000-0001-6046-8930 and Cox, Anton (2018) Modular decomposition numbers of cyclotomic Hecke and diagrammatic Cherednik algebras : a path theoretic approach. Forum of Mathematics, Sigma. e11. ISSN 2050-5094
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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Dates: |
|
Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) |
Depositing User: | Pure (York) |
Date Deposited: | 20 May 2021 15:50 |
Last Modified: | 30 Mar 2024 00:13 |
Published Version: | https://doi.org/10.1017/fms.2018.9 |
Status: | Published online |
Refereed: | Yes |
Identification Number: | https://doi.org/10.1017/fms.2018.9 |
Related URLs: |
Download
Description: MODULAR DECOMPOSITION NUMBERS OF CYCLOTOMIC HECKE AND DIAGRAMMATIC CHEREDNIK ALGEBRAS: A PATH THEORETIC APPROACH
Licence: CC-BY 2.5