Schur elements for the Ariki-Koike algebra and applications

Maria Chlouveraki (1) , Nicolas Jacon (2)

1 School of Mathematics - University of Edinburgh
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

We study the Schur elements associated to the simple modules of the Ariki-Koike algebra. We first give a cancellation-free formula for them so that their factors can be easily read and programmed. We then study direct applications of this result. We also complete the determination of the canonical basic sets for cyclotomic Hecke algebras of type $G(l,p,n)$ in characteristic $0$.

Mots clés: Schur elements; Hecke algebra; complex reflection group; Schur elements.

Domaines: Théorie des représentations [math.RT]

Maria Chlouveraki, Nicolas Jacon. Schur elements for the Ariki-Koike algebra and applications. Journal of Algebraic Combinatorics, 2012, 35 (2), pp.291-311. ⟨10.1007/s10801-011-0314-4⟩. ⟨hal-00596795⟩