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28 March 2024
 
  » arxiv » math.QA/9902087

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Ariki-Koike Algebras with Semisimple Bottoms
Jie Du ; Hebing Rui ;
Date 15 Feb 1999
Subject Quantum Algebra; Rings and Algebras MSC-class: 20C20, 20C30, 20G05, 16G99 | math.QA math.RA
AbstractWe investigated the representation thoery of an Ariki-Koike algebra whose Poincare polynomial associated with the "bottom", i.e., the subgroup on which the symmetric group acts, is non-zero in the base field. We proved that the module category of such an Ariki-Koike algebra is Morita equivalent to the module category of a direct sum of tensor products of Hecke algebras associated with certain symmetric groups. We also generalized this Morita equivalence theorem to give a Morita equivalenve between a $q$-Schur$^m$ algebra and a direct sum of tensor products of certain $q$-Schur algebras.
Source arXiv, math.QA/9902087
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