An algorithm for semistandardising homomorphisms

Suppose μ is a partition of n and λ a composition of n, and let Sμ, Mλ denote the Specht module and permutation module defined by Dipper and James for the Iwahori–Hecke algebra Hn of the symmetric group Wn. We give an explicit fast algorithm for expressing a tableau homomorphism as a linear combination of semistandard homomorphisms. Along the way we provide a utility result related to removing rows from tableaux.