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 language | English |
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Pages (from-to) | 456-510 |
Number of pages | 55 |
Journal | Journal of Algebra |
Volume | 515 |
Early online date | 22 Aug 2018 |
DOIs | |
Publication status | Published - 1 Dec 2018 |