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Generalised canonical basic sets for Ariki-Koike algebras

Abstract : Let H be a non semi-simple Ariki-Koike algebra. According to [18] and [14], there is a generalisation of Lusztig's a-function which induces a natural order (parametrised by a tuple m) on Specht modules. In some cases, Geck and Jacon have proved that this order makes unitriangular the decomposition matrix of H. The algebra H is then said to admit a "canonical basic set". We fully classify which values of m afford a canonical basic set for H and which do not. When this is the case, we describe these sets in terms of "twisted Uglov" or "twisted Kleshchev" multipartitions.
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Contributor : Thomas Gerber <>
Submitted on : Wednesday, January 22, 2014 - 3:04:38 PM
Last modification on : Friday, February 19, 2021 - 4:10:02 PM
Long-term archiving on: : Wednesday, April 23, 2014 - 5:15:32 AM


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  • HAL Id : hal-00803625, version 3
  • ARXIV : 1303.5834



Thomas Gerber. Generalised canonical basic sets for Ariki-Koike algebras. Journal of Algebra, Elsevier, 2014, 413, pp.364-401. ⟨hal-00803625v3⟩



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