2017/06/21 by C. Bowman, Bowman, C., Anton Cox +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1706.07128
openalex publication_date 2017/06/21 · openalex created_date 2017/06/30 · openalex updated_date 2026/07/28
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.