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We introduce and study some affine Hecke algebras of type ADE, generalisingthe affine Hecke algebras of GL. We construct irreducible calibratedrepresentations and describe the calibrated spectrum. This is done in terms ofnew families of combinatorial objects equipped with actions of thecorresponding Weyl groups. These objects are built from and generalise theusual standard Young tableaux, and are controlled by the considered affineHecke algebras. By restriction and limiting procedure, we obtain severalcombinatorial models for representations of finite Hecke algebras and Weylgroups of type ADE. Representations are constructed by explicit formulas, in aseminormal form.

Young tableaux and representations of Hecke algebras of type ADE