Symbolism, Imagery, Allegory
The mythic ancestor is that dude Asher keeps on having dreams about: the mysterious great-grandpa who made a ton of money for the goyische landowner before setting out to wander continental Europe on his own, teaching everyone he met about the Torah and Judaism.
Asher's relationship to his mythic ancestor is primarily one of fear and guilt. He sees in his mythic ancestor a presence much greater than himself, and doubts his ability to ever live up to it:
I was told about him so often during my very early years that he began to appear in my dreams: a man of mythic dimensions, tall, dark-bearded, powerful of mind and body; a brilliant entrepreneur; a beneficent supporter of academies of learning; a legendary traveler, and author of the Hebrew work Journeys to Distant Lands. The great man would come to me in my dreams and echo my father's queries about the latest bare wall I had decorated and the sacred margins I had that day filled with drawings. It was no joy waking up after a dream about that man. He left a taste of thunder in my mouth. (4.1)
The mythic ancestor is an important symbol in this book because he represents Asher's scholarly heritage and the hardship his father's family suffered in Europe. The mythic ancestor exists in this book in order to be juxtaposed with Asher: the fact that Asher has chosen to become an artist rather than follow the scholarly family tradition causes him to feel guilty. This guilt is partly what inspires him to paint Brooklyn Crucifixion I and II, and we know how that turns out.