Ihara's Lemma for ${\mathrm{G}\mathrm{L}}_d$: the limit case

Clozel, Harris and Taylor proposed conjectural generalizations of the classical Ihara’s lemma for ${\mathrm{G}\mathrm{L}}_2$, to higher dimensional similitude groups. We prove these conjectures in the so called limit case, which after base change is the essential one, under any hypothesis allowing level raising.