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Crystal Graphs of Higher Level q-deformed Fock Spaces, Lusztig a-values and Ariki–Koike Algebras

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Abstract

We show that the different labelings of the crystal graph for irreducible highest weight \(\mathcal{U}_q (\widehat{\mathfrak{sl}}_e)\)-modules lead to different labelings of the simple modules for non semisimple Ariki–Koike algebras by using Lusztig a-values.

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  1. Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, Besançon, France

    Nicolas Jacon

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  1. Nicolas Jacon
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Jacon, N. Crystal Graphs of Higher Level q-deformed Fock Spaces, Lusztig a-values and Ariki–Koike Algebras. Algebr Represent Theor 10, 565–591 (2007). https://doi.org/10.1007/s10468-007-9081-2

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  • DOI: https://doi.org/10.1007/s10468-007-9081-2

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