Geodesic
MODULAR DECOMPOSITION NUMBERS OF CYCLOTOMIC HECKE AND DIAGRAMMATIC CHEREDNIK ALGEBRAS: A PATH THEORETIC APPROACH
Forum of Mathematics, Sigma, Tome 6 (2018)

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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. 
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     author = {C. BOWMAN and A. G. COX},
     title = {MODULAR {DECOMPOSITION} {NUMBERS} {OF} {CYCLOTOMIC} {HECKE} {AND} {DIAGRAMMATIC} {CHEREDNIK} {ALGEBRAS:} {A} {PATH} {THEORETIC} {APPROACH}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {6},
     year = {2018},
     doi = {10.1017/fms.2018.9},
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C. BOWMAN; A. G. COX. MODULAR DECOMPOSITION NUMBERS OF CYCLOTOMIC HECKE AND DIAGRAMMATIC CHEREDNIK ALGEBRAS: A PATH THEORETIC APPROACH. Forum of Mathematics, Sigma, Tome 6 (2018). doi: 10.1017/fms.2018.9

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