Auslander–Reiten correspondence for tilting pairs

Let AA be an Artin algebra. A pair (C,T)(C,T) of AA-modules is tilting provided that CC and TT are (finitely generated) self-orthogonal, T∈addˆAC and C∈adďAT. Particularly, TT is a tilting module if and only if (A,T)(A,T) is a tilting pair. In the note, we will extend the Auslander–Reiten correspondence for tilting modules to the context of tilting pairs.