NEW ORLEANS — The New Orleans Pelicans have scuffled along for years as one of the N.B.A.’s worker-bee franchises, a respectable team but not one that has vied for championships. They lose as often as they win and play their home games in an arena called the Smoothie King Center, where a big-beaked mascot named Pierre roams the crowd.

But in recent seasons, the team has employed someone even more special: Anthony Davis, a gifted center and one of the best players in the league. Davis has a pterodactyl-length wingspan and a unibrow, which has become as much a part of his persona as his skyscraping dunks. Fans know him as “The Brow,” as if he were a superhero who draws strength from his facial hair.

New Orleans used to love him for it — until two weeks ago, when he shook the league and asked the Pelicans to trade him. The Pelicans, in return, made a bold move of their own: They refused to let him go, at least not yet.

Now Davis and New Orleans are stuck together in basketball purgatory — “It definitely is different,” said Jrue Holiday, the team’s starting point guard — and the city’s long-suffering sports fans can only wonder: What do we do now?