well technically posterior deltoid does transverse extension and extension... tho it also does transverse abduction (reverse flye's etc..) and lateral rotation.. extension isnt posterior delts main function.. its just helping there minimally while latissimus dorsi, teres major etc do most of the work. Also for lateral rotation its not its main function. Rotator cuff muscle group handles majority of that. again posterior delt is just synergist there. Could say transverse extension and transverse abduction are its "main" functions aka lateral movement away from the midline of the body in a horizontal plane. either moving the upper arm away from the chest with the elbows facing down or moving the upper arm away from the chest with the elbows out to the sides. Good examples of transverse abduction would be reverse flyes while for transverse extension would be facepull. extension happens abit when you do straight arm pulldowns.