Graded decomposition numbers of Ariki-Koike algebras for blocks of small weight

2013/08/09 by Sinéad Lyle, Sinead Lyle, Lyle, Sinead +2
Mathematics · #20C08 #20C30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT #msc:20C08 #msc:20C30

paper · pdf · doi:10.48550/arxiv.1308.2170

26 pages, final version, to appear in Journal of Pure and Applied Algebra

openalex publication_date 2013/08/09 · arxiv created 2015/09/10 · arxiv updated 2015/09/11 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We present some blocks of Ariki-Koike algebras H_n,r for which the decomposition matrices are independent of the characteristic of the underlying field. We complete the description of the graded decomposition numbers for blocks of Ariki-Koike algebras of weight at most two, which consists of analysing the indecomposable core blocks at level r = 3, and give a closed formula for the decomposition numbers in this case.

Citations

• 2-Kac-Moody algebras

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