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Young tableaux and representations of Hecke algebras of type ADE. (English) Zbl 1483.20008

Summary: We introduce and study some affine Hecke algebras of type ADE, generalising the affine Hecke algebras of GL. We construct irreducible calibrated representations and describe the calibrated spectrum. This is done in terms of new families of combinatorial objects equipped with actions of the corresponding Weyl groups. These objects are built from and generalise the usual standard Young tableaux, and are controlled by the considered affine Hecke algebras. By restriction and limiting procedure, we obtain several combinatorial models for representations of finite Hecke algebras and Weyl groups of type ADE. Representations are constructed by explicit formulas, in a seminormal form.

MSC:

20C08 Hecke algebras and their representations
05E10 Combinatorial aspects of representation theory
05E16 Combinatorial aspects of groups and algebras
20C30 Representations of finite symmetric groups
20F55 Reflection and Coxeter groups (group-theoretic aspects)
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