Specht modules labelled by hook bipartitions I

摘要

Brundan, Kleshchev and Wang equip the Specht modules S-lambda over the cyclotomic Khovanov-Lauda-Rouquier algebra H-n(A) with a homogeneous Z-graded basis. In this paper, we begin the study of graded Specht modules labelled by hook bipartitions ((n- m), (1(m))) in level 2 of H-n(A), 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 psi(1), ... ,psi(n-1) on the basis elements of S((n - m),(1(m))). 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. (C) 2018 Elsevier Inc. All rights reserved.