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arXiv · 1812.08546

On the number of constituents of induced modules of Ariki-Koike algebras

Christoph Schoennenbeck
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Abstract

We examine the crystal graph of the $\widehat{\mathfrak{sl}}_e$-module arising from an $\widehat{\mathfrak{sl}}_e$-categorification to study the defining endo-functors of the categorification. This yields lower bounds on the number of irreducible constituents of certain objects. We use Ariki's categorification result on Ariki-Koike algebras to obtain a new lower bound on the number of constituents of their parabolically induced modules. In particular this will imply reducibility of every induced module.

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BibTeXRIS

Christoph Schoennenbeck. 2018-12-20. On the number of constituents of induced modules of Ariki-Koike algebras. https://arxiv.org/abs/1812.08546

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