Specht modules labelled by hook bipartitions I

Louise Sutton

Research output: Contribution to journalArticlepeer-review

Abstract

Brundan, Kleshchev and Wang equip the Specht modules $S_{\lambda}$ over the cyclotomic Khovanov–Lauda–Rouquier algebra $\mathscr{H}_n^\{Lambda}$ with a homogeneous $\mathbb{Z}$-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 $\mathscr{H}_n^\{Lambda}$, 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 $\psi_1,\dots,\psi_{n-1}$ 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.
Original languageEnglish
Pages (from-to)456-510
Number of pages55
JournalJournal of Algebra
Volume515
Early online date22 Aug 2018
DOIs
Publication statusPublished - 1 Dec 2018

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