2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129237The structure of subring $J^{Γ\cap Γ^{-1}}$ of the asymptotic Hecke algebra is described for $Γ$ a left cell of the Coxeter group of type $H_4$. A small set of generators is produced. The subalgebras spanned by a subset of the basis ${t_x}_{x\in Γ\capΓ^{-1}}$ are determined.Representation TheoryRings and Algebrastext