Abstract
Let Sλ denote the Specht module defined by Dipper and James for the Iwahori–Hecke algebra Hn of the symmetric group Sn. When e=2 we determine the decomposability of all Specht modules corresponding to hook partitions (a,1b). We do so by utilising the Brundan–Kleshchev isomorphism between H and a Khovanov–Lauda–Rouquier algebra and working with the relevant KLR algebra, using the set-up of Kleshchev–Mathas–Ram. When n is even, we easily arrive at the conclusion that Sλ is indecomposable. When n is odd, we find an endomorphism of Sλ and use it to obtain a generalised eigenspace decomposition of Sλ.
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