MODULAR DECOMPOSITION NUMBERS OF CYCLOTOMIC HECKE AND DIAGRAMMATIC CHEREDNIK ALGEBRAS: A PATH THEORETIC APPROACH
Keyword(s):
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.
2001 ◽
Vol 71
(2)
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pp. 201-210
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Keyword(s):
1985 ◽
Vol 292
(1)
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pp. 123-123
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2015 ◽
Vol 16
(5)
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pp. 987-1074
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2014 ◽
Vol DMTCS Proceedings vol. AT,...
(Proceedings)
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2015 ◽
Vol DMTCS Proceedings, 27th...
(Proceedings)
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1996 ◽
Vol 119
(3)
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pp. 383-402
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