Certainly Emily is defined by her autocratic father who represents the autocratic Old South. In the second paragraph, the reader learns that
Miss Emily had gone to join the representatives of those august names where they lay in in the cedar-bemused cemetery among the ranked...gaves of...[those] who fell at the battle of Jefferson.
After her father's death, Emily is unable to adjust to the New South and lives in the past: "Alive, Miss Emily had been a tradition,...a sort of hereditary obligation upon the town...." She refuses to pay taxes believing that the arrangement made long ago by her father continues. She "vanquishes" the town authorities when they call upon her, just as she vanquishes the ladies who call upon her as well as her relatives. However, Miss Emily is left alone.
Being left alone, and a pauper, she had become humanized. Now she too would know...the old despair of a penny more or less....
Still suffering from the loss of her father and his world, Emily "clings to that which had robbed her" and becomes ill--both signs of despair and depression. Out of her despairing loneliness she takes on a lover, Homer Barron, a man who is a the center of "a lot of laughing," but he is not the type of man that the town expects Miss Emily to court: "...there were others...who said that even grief could not cause a real lady to forget noblesse oblige."
It is an act of feverish despair that causes Emily to poison Homer again in an effort to "cling to that which had robbed her."
Emily's father was an overbearing protector of Emily who did not allow her to marry. This overprotection left Emily unprepared to deal with the real world. This is shown when Emily refuses to let go of her father by allowing his body to be buried. She lost the only man really close to her and I'm sure this contributed to her despair. Not only did she lose him, but her father left her virtually penniless with no marketable skills. This really shows a total disregard for his daughter and I'm sure it made life even more unbearable. This contributes to her overwhelming desire to marry Homer Barron, despite the fact he was gay. When he refuses to marry, she simply kills him so he cannot escape her. Unlike her father, who was finally taken away, Homer can be with her forever.