On the Mullineux involution for Ariki-Koike algebras
Nicolas Jacon (LM-Besan\c{c}on), C\'edric Lecouvey (LMPA)
TL;DR
This paper generalizes the Mullineux involution for Ariki-Koike algebras and introduces an efficient algorithm for its computation that avoids complex affine crystal path calculations.
Contribution
It provides a novel, efficient algorithm for the generalized Mullineux involution in Ariki-Koike algebras, simplifying previous computational methods.
Findings
Algorithm efficiently computes the involution without affine crystal paths
Generalization extends Mullineux involution to Ariki-Koike algebras
Reduces computational complexity in representation theory
Abstract
This note is concerned with a natural generalization of the Mullineux involution for Ariki-Koike algebras. Using a result of Fayers together with previous results by the authors, we give an efficient algorithm for computing this generalized Mullineux involution. Our algorithm notably does not involve the determination of paths in affine crystals.
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