The character is question is Arisia Rrab. Arisia was a elfin-looking Green Lantern who was 13 years old. She would do things like design new outfits for the other Lanterns and hang around Jordan. Jordan told her to beat it before she got him in trouble.
What changed? She did. Literally. Because the power rings react to will, Arisia literally willed herself to become older. Well, sort of. Her body developed into sexual maturity, although her mind and actual age was still that of a 13 year old.
Jordan didn't put up any resistance to this. He gleefully jumped into an affair with her. And when the other Lanterns were basically saying, "Uh, dude? She's still a 13 year old," Jordan told them to jam it.
This went on for a while and they eventually broke up. The character was created by Mike W. Barr, who is a fan of the manly men writing thing, so I imagine he was trying to make Jordan a mack daddy. But every time I see Arisia, all I can think is she's 13 and Chris Hansen should be telling Jordan, "Why don't you have a seat over there?"