Decomposition numbers for Rouquier blocks of Ariki-Koike algebras I

Lyle, Sinead ORCID: https://orcid.org/0000-0002-6032-7721 (2024) Decomposition numbers for Rouquier blocks of Ariki-Koike algebras I. Journal of Combinatorial Algebra. ISSN 2415-6302

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Abstract

Let H=Hr,n​(q,Q) denote an Ariki–Koike algebra over a field of characteristic p≥0. For each r-multipartition λ of n, there exists a H-module Sλ and for each Kleshchev r-multipartition μ of n, there exists an irreducible H-module Dμ. Given a multipartition λ and a Kleshchev multipartition μ both lying in a Rouquier block such that λ and μ have the same multicore, we give a closed formula for the graded decomposition number [Sλ:Dμ]v​ when p=0 or when each component of μ has fewer than p removable e-rim hooks.

Item Type:	Article
Uncontrolled Keywords:	ariki-koike algebras,decomposition numbers,rouquier blocks
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics
Depositing User:	LivePure Connector
Date Deposited:	24 May 2024 15:30
Last Modified:	26 May 2024 06:31
URI:	https://ueaeprints.uea.ac.uk/id/eprint/95305
DOI:	10.4171/JCA/87

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