Decomposition numbers for Rouquier blocks of Ariki-Koike algebras I

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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.
Original languageEnglish
JournalJournal of Combinatorial Algebra
Early online date12 Mar 2024
DOIs
Publication statusE-pub ahead of print - 12 Mar 2024

Keywords

  • Ariki-Koike algebras
  • decomposition numbers
  • Rouquier blocks

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