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In this chapter, we phrase Lusztig and Andersen’s conjectures in their original group theoretic context. All of the material we consider here is “classical” in the sense that it is over 25 years old and makes no mention of categorification whatsoever, it is all entirely group theoretic.We recall the most salient points regarding the representation of the symmetric groups and their Schur algebras, both in the language of tableaux and the language of alcove geometries, hence arriving at the conjectures of Andersen and Lusztig within the latter context.

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Reformulating Lusztig’s and Andersen’s conjectures

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  • 发表日期：

    2025年

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  • Chris Bowman

摘要

In this chapter, we phrase Lusztig and Andersen’s conjectures in their original group theoretic context. All of the material we consider here is “classical” in the sense that it is over 25 years old and makes no mention of categorification whatsoever, it is all entirely group theoretic.We recall the most salient points regarding the representation of the symmetric groups and their Schur algebras, both in the language of tableaux and the language of alcove geometries, hence arriving at the conjectures of Andersen and Lusztig within the latter context.