Is it permissible for someone who has committed a major sin to lead the prayer?

The person leading the prayer must possess the qualifications for imamate. It is not permissible for someone who cannot recite the Qur’an, does not know how to perform the prayer, is not of sound mind, or is a child who has not reached puberty to lead the prayer.

As long as a Muslim does not consider what is forbidden to be lawful or what is lawful to be forbidden, even if they have committed a major sin, they may lead the prayer; the prayer performed behind them is valid. The Prophet (peace be upon him) said, “Pray behind every Muslim, whether righteous or sinful (pious or sinful).” (Dârekutnî, es-Sünen, 2/404 [1768]; see also Abû Dâwûd, Salât, 64 [594]; Jihâd, 34 [2533]). This hadith establishes a principle: any believer who possesses the minimum knowledge required to lead the prayer may do so. (Serahsî, Sharh al-Siyar al-Kabir, 1/156-157; Ibn Nujaym, al-Bahr, 1/370) However, it is preferable for the imam to be someone who avoids sin, is loved by the congregation, and has good character. According to the Hanafi, Shafi’i, and Maliki schools, if someone with these qualities is present, it is disliked (makruh) for a fasiq—that is, someone who openly commits major sins or persists in minor sins—to lead the prayer. (Ibn al-Humam, Fath al-Qadir, 1/350; Ibn Abidin, Radd al-Muhtar, 1/560; Harashi, Sharh Mukhtasar, 2/23)

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu