Schur elements for the Ariki-Koike algebra and applications
Maria Chlouveraki, Nicolas Jacon (LM-Besan\c{c}on)
TL;DR
This paper provides a new cancellation-free formula for Schur elements of the Ariki-Koike algebra, facilitating their computation and applications, and completes the classification of canonical basic sets for certain cyclotomic Hecke algebras.
Contribution
It introduces a simplified formula for Schur elements and advances the understanding of basic sets in cyclotomic Hecke algebras of type G(l,p,n).
Findings
Derived a cancellation-free formula for Schur elements.
Applied the formula to determine canonical basic sets.
Enhanced computational methods for Ariki-Koike algebra representations.
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 in characteristic 0.
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