A Specht filtration of an induced Specht module

Let \H_n be a (degenerate or non-degenerate) Hecke algebra of type $G(\mathrm{\ell },1,n)$, defined over a commutative ring $R$ with one, and let $S(\text{bmu})$ be a Specht module for \H_n. This paper shows that the induced Specht module S(\bmu)\otimes_{\H_n}\H_{n+1} has an explicit Specht filtration.