Decomposition numbers for Rouquier blocks of Ariki-Koike algebras I

Abstract

Let $\mathcal{H}$ denote an Ariki-Koike algebra over a field of characteristic $p\ge 0$. For each $r$-multipartition $\lambda$ of $n$, we define a $\mathcal{H}$-module $S^{\lambda }$ and for each Kleshchev $r$-multipartition $\mu$ of $n$, we define an irreducible $\mathcal{H}$-module $D^{\mu }$. Given a multipartition $\lambda$ and a Kleshchev multipartition $\mu$ both lying in a Rouquier block and which have a common multicore, we give a closed formula for the graded decomposition number $[S^{\lambda }:D^{\mu }{]}_v$ when $p=0$.

arXiv comment25 pages