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Canonical basic sets in type B

Meinolf Geck·Nicolas Jacon
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Abstract

More than 10 years ago, Dipper, James and Murphy developped the theory of Specht modules for Hecke algebras of type $B\_n$. More recently, using Lusztig's a-function, Geck and Rouquier showed how to obtain parametrisations of the irreducible representations of Hecke algebras (of any finite type) in terms of so-called canonical basic sets. For certain values of the parameters in type $B\_n$, combinatorial descriptions of these basic sets were found by Jacon, based on work of Ariki and Foda-Leclerc-Okado-Thibon-Welsh. Here, we consider the canonical basic sets for all the remaining choices of the parameters.

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Meinolf Geck, Nicolas Jacon. 2006-03-24. Canonical basic sets in type B. https://arxiv.org/abs/math/0601104

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