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.
| Original language | English |
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| Article number | e11 |
| Journal | Forum of Mathematics, Sigma |
| Volume | 6 |
| Early online date | 3 Jul 2018 |
| DOIs | |
| Publication status | E-pub ahead of print - 3 Jul 2018 |