Abstract
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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
