A Specht filtration of an induced Specht module

Let Hn be a (degenerate or non-degenerate) Hecke algebra of type G(ℓ,1,n), defined over a commutative ring R with one, and let S(μ) be a Specht module for Hn. This paper shows that the induced Specht module S(μ)⊗HnHn+1 has an explicit Specht filtration.