This polity feuded on its east with (*) Kuchlug, who had destroyed its earlier enemy, the Karakitai empire.  
Mahmud Yalavach was sent as envoy to this polity, which had been his birthplace, and this polity was paid tribute by Sa'd ibn Zangi, the Salghurid atabeg of Shiraz.  An attempt to revive this polity established a capital at Tabriz and was led by the ruler who had earlier won at the Battle of Parwan before being defeated at the Indus, Jalal al-Din.  The downfall of this polity began when one of its vassals, Inalchuq, the governor of Otrar, killed the members of a caravan, after which the ruler of this polity beheaded some ambassadors and shaved their beards.  This polity feuded on its east with (*) Kuchlug, who had destroyed its earlier enemy, the Karakitai empire.  Its first ruler, Anustegin Gharacha'i, was originally a slave of Malik-Shah and thus came to power as a vassal of the Seljuks, while it reached its greatest extent under Shah Muhammad II.  For 10 points, name this empire that controlled much of Persia and central asia in the early 13th century before being conquered by Genghis Khan, originally centered in modern Uzbekistan. 
Mahmud Yalavach was sent as envoy to this polity, which had been his birthplace, and this polity was paid tribute by Sa'd ibn Zangi, the Salghurid atabeg of Shiraz.  
{Khwarezmid} empire [or {Khwarezmian} empire; or {Khwarezm}-{Shah dynasty}]