The Sri Vaishnava sect has two sub-sects, Thenkalai and Vadakalai. Vadakalais follow the teachings of Vedanta Desikan, whereas Thenkalais follow the teachings of Pillai Lokacharya. I just found an interesting connection between Vedanta Desikan and Pillai Lokacharya.
The largest Vadakalai Matham is Ahobilam Matham. As you can see in the picture below, it has three Guru Paramparas, a Samashrayana Parampara, a Kalakshepa Parampara, and a Sanyasa Parampara. That's because its founder Adivan Sadagopan: one guru who gave him Samashrayanam (initiation into Pancharatra), one guru who gave him Kalakshepam (knowledge), and one guru (Lord Narasimha) who gave him Sanyasa:
If you look on the left side, you'll see that Adivan Sadagopan's Samashrayana Parampara originates from Vadakku Thiruveedhi Pillai, the father of Pillai Lokacharya. And the name below it is Rangacharya. I found some interesting information about him from this chart published by Sri Rangam Andavan Ashramam. His full name is Kidambi Rangacharya. You see, Vedanta Desikan's mother came from a Swayamacharya family called the Kidambi family, descended from Ramanujacharya's cook Kidambi Achan. And Vedanta Desikan had two maternal uncles, Kidambi Apullar and Kidambi Rangacharya. It was Kidambi Apullar who served as Vedanta Desikan's guru. Now Kidambi Apullar, being a Swayamacharya person, received Samashrayanam from his father, but received Kalakshepam (knowledge) from a famous Sri Vaishnava Acharya named Nadadur Ammal.
But it seems that Kidambi Apullar's brother Kidambi Rangacharya received Samashrayanam from Pillai Lokacharya's father Vadakku Thiruveedhi Pillai. My question is, why did Kidambi Rangacharya receive Samashrayanam from Vadakku Thiruveedhi Pillai? I can understand if, like his brother Kidambi Apullar, he received knowledge from outside his own family. But why, being a Swayamacharya person whose father was in a position to give Samashrayanam, did he receive Samashrayanam from outside his own family?
Is there a story behind this?