Discuss the ghost's role in "A Rose for Emily."

There are many ghosts in "A Rose for Emily," including the ghost of Miss Emily's father, of Homer, and of her family's former elevated status. First, there is the ghost of Miss Emily’s father. Although the story never indicates the presence of his spirit, Miss Emily holds onto his body for days after his death and will not allow the townspeople into her home to take his body for burial. Miss Emily lives with his physical presence after his passing and presumably lives under his authority too, thus reflecting both a figurative and literal retention of his ghost.

When she finally falls in love with Homer, Miss Emily must be aware of how disapproving her father would be of the relationship, as Homer is not her equal in terms of status, even though Emily’s family long ago lost its money. Yet, she is able to break free of her father's disapproval, or her perceived disapproval in her mind, finally breaking free of his ghost.

The most important ghost is Homer's. The ghost of their relationship hangs over Miss Emily in the townspeople’s minds and in their gossip for a very long time after he “leaves” her. She retains Homer’s decaying body after she murders him and presumably lives with his ghost, most likely interacting with him—or his ghost—in her mind for years after his death.

Who or what represent the ghosts in "A Rose for Emily"?

What an interesting question.  I would argue that the ghosts that exist in this story are the ghosts of tradition.  The community Emily is a part of is resistant to change, as much of the South was following the Civil War.  As most humans, they cling to what they have already known.  They cling to laws and traditions that no longer exist.  For example, Emily clings to the tradition that allowed her not to pay taxes.  That tradition died with Colonel Sartoris, but she clings to the ghost of it nonetheless.  And the new town leaders, the younger set, are so influenced by these ghosts of tradition that they do not enforce their own laws.  Clearly, the ghosts exist and are powerful.