An algorithm for semistandardising homomorphisms

Abstract

Suppose $\mu$ is a partition of $n$ and $\lambda$ a composition of $n$, and let $S^{\mu }$, $M^{\lambda }$ denote the Specht module and permutation module defined by Dipper and James for the Iwahori--Hecke algebra ${\mathcal{H}}_n$ of the symmetric group ${\mathfrak{S}}_n$. We give an explicit fast algorithm for expressing a tableau homomorphism ${\hat{\varphi }}_A:S^{\mu }\to M^{\lambda }$ as a linear combination of semistandard homomorphisms. Along the way we provide a utility result related to removing rows from tableaux.

References in corpus (1)

• Some new decomposable Specht modules

Cited by in corpus (3)

• Some new decomposable Specht modules
• The irreducible representations of the alternating group which remain irreducible in characteristic p
• The reducible Specht modules for the Hecke algebra ${\mathcal{H}}_{\mathbb{C},-1}({\mathfrak{S}}_n)$