Specht modules labelled by hook bipartitions I

Brundan, Kleshchev and Wang equip the Specht modules Sλ over the cyclotomic Khovanov-Lauda-Rouquier algebra HnΛ with a homogeneous Z-graded basis. In this paper, we begin the study of graded Specht modules labelled by hook bipartitions ((n−m),(1m)) in level 2 of HnΛ, which are precisely the Hecke algebras of type B, with quantum characteristic at least three. We give an explicit description of the action of the Khovanov-Lauda-Rouquier algebra generators ψ1,…,ψn−1 on the basis elements of S((n−m),(1m)). Introducing certain Specht module homomorphisms, we construct irreducible submodules of these Specht modules, and thereby completely determine the composition series of Specht modules labelled by hook bipartitions.