Cyclotomic $q$-Schur algebras associated to the Ariki-Koike algebra

Simple item page
dc.creatorShoji, Toshiaki
dc.creatorWada, Kentaro
dc.date2007-07-12
dc.date.accessioned2026-07-07T08:16:12Z
dc.date.available2026-07-07T08:16:12Z
dc.descriptionLet $S$ be the cyclotomic $q$-Schur algebra associated to the Ariki-Koike algebra $H_{n,r}$ of rank $n$, introduced by Dipper-James-Mathas. For each $p = (r_1, ..., r_g)$ such that $r_1 + ... + r_g = r$, we define a subalgebra $S^p$ of $S$ and its quotient algebra $\bar S^p$. It is shown that $S^p$ is a standardly based algebra and $\bar S^p$ is a cellular algebra. By making use of these algebras, we show that certain decomposition numbers for $S$ can be expressed as a product of decomposition numbers for cyclotomic $q$-Schur algebras associated to smaller Ariki_koike algebras $H_{n_k,r_k}$.
dc.description43 pages
dc.identifierhttps://arxiv.org/abs/0707.1733
dc.identifierhttp://arxiv.org/abs/0707.1733
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133700
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.subject20C08, 20C20, 20G05
dc.titleCyclotomic $q$-Schur algebras associated to the Ariki-Koike algebra
dc.typetext

Files

Collections

arXiv