On J-folded alcove paths and combinatorial representations of affine Hecke algebras

2022/12/21 by Jérémie Guilhot, Guilhot, Jérémie, Eloise Little +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2212.10781

openalex publication_date 2022/12/21 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28

Abstract

We introduce the combinatorial model of J-folded alcove paths in an affine Weyl group and construct representations of affine Hecke algebras using this model. We study boundedness of these representations, and we state conjectures linking our combinatorial formulae to Kazhdan-Lusztig theory and Opdam's Plancherel Theorem.

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