Poulain d’Andecy, Loïc Young tableaux and representations of Hecke algebras of type ADE. (English) Zbl 1483.20008 J. Comb. Algebra 1, No. 4, 371-423 (2017). 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. Cited in 1 Document 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) Keywords:Hecke algebras; Weyl groups; simply-laced root systems; affine Hecke algebras; Jucys-Murphy elements; skew partitions; Young tableaux; seminormal representations; calibrated representations PDFBibTeX XMLCite \textit{L. Poulain d'Andecy}, J. Comb. Algebra 1, No. 4, 371--423 (2017; Zbl 1483.20008) Full Text: DOI arXiv