Schur elements for the Ariki-Koike algebra and applications

Abstract

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.

The paper contains the results of arXiv:1101.1465

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• Fusion Procedure for Cyclotomic Hecke Algebras
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• An isomorphism theorem for degenerate cyclotomic Yokonuma-Hecke algebras and applications
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• Rational Catalan Numbers for Complex Reflection Groups