The Green correspondence for the representations of Hecke algebras of type $A\sb {r-1}$
The Green correspondence for the representations of Hecke algebras of type $A\sb {r-1}$
We first prove the conjecture mentioned by Leonard K. Jones in his thesis. By applying this conjecture, we obtain that the vertex of an indecomposable ${\mathcal {H}_F}$-module is an $l$-parabolic subgroup. Finally, we establish the Green correspondence for the representations of Hecke algebras of type ${A_{r - 1}}$.