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Graded Specht modules

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arxiv 0901.0218 v3 pith:BDCK4XTZ submitted 2009-01-02 math.RT

Graded Specht modules

Jonathan Brundan , Alexander Kleshchev , Weiqiang Wang This is my paper
classification math.RT
keywords algebrasmodulesspechtauthorscyclotomicdefinedexplainfirst
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Recently, the first two authors have defined a Z-grading on group algebras of symmetric groups and more generally on the cyclotomic Hecke algebras of type G(l,1,d). In this paper we explain how to grade Specht modules over these algebras.

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  1. Kleshchev multipartitions, affine Mirkovi\'c-Vilonen polytopes, and representations of KLR algebras in type ${\tt A}^{(1)}_1$

    math.RT 2026-05 unverdicted novelty 6.0

    Explicit isomorphisms are built between three models of the B(∞) crystal in type A1^(1), including a new upper ledge diagram model, plus applications to KLR algebra branching rules.