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