Dipper-James-Murphy's conjecture for Hecke algebras of type B

Susumu Ariki (1) , Nicolas Jacon (2)

1 RIMS - Research Institute for Mathematical Sciences
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

We prove a conjecture by Dipper, James and Murphy that a bipartition is restricted if and only if it is Kleshchev. Hence the restricted bipartitions naturally label the crystal graphs of level two irreducible integrable $\mathcal{U}_v({\widehat{\mathfrak{sl}}_e})$-modules and the simple modules of Hecke algebras of type $B_n$.

Domaines: Théorie des représentations [math.RT]

Susumu Ariki, Nicolas Jacon. Dipper-James-Murphy's conjecture for Hecke algebras of type B. 2007. ⟨hal-00136680v3⟩