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In this paper, we prove a higher dimensional version of Auslander-Iyama-Solberg correspondence. Iyama and Solberg have shown a bijection between -minimal Auslander-Gorenstein algebras and -precluster tilting modules. If is an -minimal Auslander-Gorenstein algebra, then the pair is a relative -Auslander-Gorenstein pair in the sense of the authors, where is the minimal faithful projective-injective left -module. We establish a higher dimensional Auslander-Iyama-Solberg, where is replaced by any self-orthogonal module having finite projective and injective dimension. This new correspondence provides a bijection between relative Auslander--Gorenstein pairs and a new class of objects that generalise precluster tilting modules. This way, we obtain a new correspondence coming from the modular representation theory of general linear groups.