In this excerpt from the Garuda Purana, various incarnations of Vayu the wind god are described. In particular, it says this:
When lord Rama incarnated on earth, Vayu was born as Hanuman for rendering assistance to Rama. When lord Krishna descended on earth, he was born as Bhima, the offspring of Vayu. Vayu will be born as Maniman daitya, known as Shankara. He will be so called, for he will abolish caste and destroy Dharma.
Now I think the part in bold is probably either the source or the product of Madhvacharya's belief that Adi Shankaracharya was a rebirth of a demon, described in this book:
Madhva believed himself to be an incarnation of Vayu, and probably as a result of Shankarite persecution, he taught that Shankara was a reincarnation of obscure demon named Manimat who appears in the Mahabharata.
In the Vana Parva of the Mahabharata, Bhima kills a demon named Manimat. Since Madhvacharya considered himself to be an incarnation of Vayu, he thought he was the rebirth of Bhima and Adi Shankaracharya was the rebirth of Manimat. For the record I find this whole line of thinking absurd; I consider Adi Shankaracharya to be an incarnation of Shiva as I discuss here. And besides, that Garuda Purana chapter identifies Shankara, not Madhva, as an incarnation of Vayu.
But I'm interested in a statement found later on in that chapter. The Garuda Purana also describes the incarnations of Vayu's wife Bharati, and in particular it says this:
Draupadi, the daughter of Drupada gave up her body together with her maidens. O lord of birds, she will be born in the Kali Yuga in the house of Shankara in the village of Karati.
Now Karati is the actual birthplace of Adi Shankaracharya. So my question is, who is this rebirth of Draupadi supposed to be?
The fact that she was born "in the house of Shankara" might indicate that she was Adi Shankaracharya's sister or something. But then again, if Adi Shankaracharya is being considered an incarnation of Vayu and this woman is being considered an incarnation of Vayu's wife Bharati, then the logical relation would be that of husband and wife. But the traditional biographies of Adi Shankaracharya make clear that he took up Sanyasa at a you age.
Is it possible that before he had become a Sanyasi, his mother was planning to have him marry some girl? Are there any biographies of Adi Shankracharya that shed light on who this rebirth of Draupadi may be?