Crystal graphs of irreducible $U_v(\hat{sl}_e)$-modules of level two and Uglov bipartitions

Abstract

We give a simple description of the natural bijection between the set of FLOTW bipartitions and the set of Uglov bipartitions (which generalizes the set of Kleshchev bipartitions). These bipartitions, which label the crystal graphs of irreducible $\mathcal{U}\_v({\hat{\mathfrak{sl}}\_e})$-modules of level two, naturally appear in the context of the modular representation theory of Hecke algebras of type $B\_n$.