Auslander–Reiten conjecture for Auslander-Gorenstein algebras

Let $A$ be an algebra satisfying the Auslander condition, meaning that it is $n$-Gorenstein for every $n\geq 1$. Auslander–Reiten conjecture. If $A$ satisfies the Auslander condition, then $A$ is Auslander-Gorenstein. This is the main open homological conjecture related to Auslander-Gorenstein algebras. Auslander and Reiten formulated it as a question; under the same hypotheses, it is equivalent to the question of whether finite finitistic dimension implies being Iwanaga-Gorenstein.