Is it permissible to pray behind an imam whose adultery has been clearly and unequivocally proven?

You must choose another Imam from among the people of righteousness and goodness, while striving to reform him and urge him to repent. If he does not repent, then stop praying behind him and pray behind another Imam if one is available. If no other Imam is available, or if the other mosque is far away, then your prayer is valid according to the preponderant opinion of the scholars who validate prayer behind innovators (Mubtadi'ah) and transgressors (Fussaq), just as some Companions (Sahabah) used to pray behind Al-Hajjaj.