Qutlugh-Khanids
The Qutlugh-Khanids was a culturally Persianate dynasty of ethnic Khitan origin that ruled over Kirman from 1222 to 1306.
It was founded by Buraq Hajib, who emigrated from the Qara Khitai during the collapse of the realm. Originally an independent entity, the Qutlugh-Khanid dynasty subsequently ruled as vassals of the Khwarazmian Empire, the Mongol Empire and the Ilkhanate. The dynasty was removed from power by the Ilkhanid ruler Öljaitü, who appointed Nasir al-Din Muhammad ibn Burhan as governor of Kirman.
Although there was no mention of a dynasty called the "Later Western Liao" in traditional Chinese scholarship, historian Wang Zhilai wrote a paper On the Later Western Liao in 1983, where he proposed to call the Qutlugh-Khanids the "Later Western Liao", thereby positioning the dynasty as an extension of the Western Liao.
End of the Kirmanid dynasty
The Mongol Ilkhanid ruler Öljaitü ended the Kirman Kara-Khitan dynasty in 1306 after the last of the Qutlugh Khans, Quțb al-Dīn II, neglected to pay his dues to the Mongol treasury. The Qutlugh Khan escaped to Shiraz, and his daughter later became the wife of Mubariz al-Din Muhammad, the founder of the Muzaffarid dynasty.