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

Jérémie Guilhot; Eloise Little; James Parkinson

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

Representation Theory 2024-10-17 v4

Authors: Jérémie Guilhot , Eloise Little , James Parkinson

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.

Keywords

j-folded alcove paths affine weyl group affine hecke algebras combinatorial representations kazhdan-lusztig theory

Cite

@article{arxiv.2212.10781,
  title  = {On $J$-folded alcove paths and combinatorial representations of affine Hecke algebras},
  author = {Jérémie Guilhot and Eloise Little and James Parkinson},
  journal= {arXiv preprint arXiv:2212.10781},
  year   = {2024}
}

Comments

To appear in Algebras and Representation Theory, sections renumbered to agree with published version

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

Abstract

Keywords

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