It's common knowledge (and stated in the movie) that O, Brother, Where Art Thou? is based on the Greek Epic The Odyssey by Homer.
Most of the O, Brother characters have parallels in The Odyssey. But I can't find anyone who seems to match the bank robber George 'Babyface' Nelson.
George Nelson was a real bank robber, so it's possible he was just part of the story, and wasn't necessarily taken from The Odyssey... but I'm hoping there's a connection I'm missing.