On decomposition numbers of the cyclotomic q-Schur algebras
| dc.creator | Sawada, Nobuharu | |
| dc.date | 2005-10-21 | |
| dc.date.accessioned | 2026-07-07T06:47:45Z | |
| dc.date.available | 2026-07-07T06:47:45Z | |
| dc.description | Let $S(Λ)$ be the cyclotomic q-Schur algebra associated to the Ariki-Koike algebra $H$. We construct a certain subalgebra $S^0(Λ)$ of $S(Λ)$, and show that it is a standardly based algebra in the sense of Du and Rui. $S^0(Λ)$ has a natural quotient $\bar{S^0}(Λ)$, which turns out to be a cellular algebra. In the case where the modified Ariki-Koike algebra $H^{\flat}$ is defined, $\bar{S^0}(Λ)$ coincides with the cyclotomic q-Schur algebra associated to $H^{\flat}$. In this paper, we discuss a relationship among the decomposition numbers of $S(Λ)$, $S^0(Λ)$ and $\bar{S^0}(Λ)$. In particular, we show that some important part of the decomposition matrix of $S(Λ)$ coincides with a part of the decomposition matrix of $\bar{S^0}(Λ)$. | |
| dc.identifier | https://arxiv.org/abs/math/0510457 | |
| dc.identifier | http://arxiv.org/abs/math/0510457 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103758 | |
| dc.subject | Representation Theory | |
| dc.subject | 20C08; 20C20 | |
| dc.title | On decomposition numbers of the cyclotomic q-Schur algebras | |
| dc.type | text |