Robert Browning’s poem explores narcissism through the character of the duke. The duke is the first-person narrator. One aspect of Browning’s characterization that points to narcissism is the duke’s excessive references to himself and his possessiveness. He begins the poem by referring to the painting’s subject as belonging to him, saying, “That’s my last duchess.”

He continues by talking about how he commissioned the portrait, naming a famous and no doubt expensive artist. Continuing on, he mentions the kinds of inquiries that other viewers have made. His exclusive rights to conceal or reveal the portrait also point to his self-centered attitude. Viewers by themselves cannot figure out how it came to be; instead,

But to myself they turned (since none puts by
The curtain I have drawn for you, but I)….

The duke’s jealousy includes all other men, but especially targets the painter. He seems to think that he should be able to control the duchess’s feelings. In holding that view, he reveals that he does not regard her as an equal person. One indication of his fixation on self-interest and utter lack of empathy is his reference to his title and ancient family lineage.

She thanked men…
as if she ranked
My gift of a nine-hundred-years-old name|With anybody’s gift.

Similarly, he refers to his pride and unwillingness to compromise.

Who’d stoop to blame
This sort of trifling?...
E’en then would be some stooping; and I choose
Never to stoop.

The term “narcissism” means being extremely self-centered and concerned with one’s own reputation or appearance. It is derived from the ancient Greek mythological figure Narcissus. He was a youth who fell in love with his own reflection when he saw it in a pool.Upon seeing himself he thought he saw a handsome other person; his vanity led to his being turned into a flower by Nemesis (in Metamorphoses).

The story stimulated Sigmund Freud’s naming of a type of neurosis, which he explored in his 1914 work On Narcissism. Excessive, continued self-love becomes problematic if it continues long past the early developmental stage of infancy. The Mayo Clinic website defines narcissistic personality disorder, which was identified in the 1960s, as

a mental condition in which people have an inflated sense of their own importance, a deep need for excessive attention and admiration, troubled relationships, and a lack of empathy for others. But behind this mask of extreme confidence lies a fragile self-esteem that's vulnerable to the slightest criticism.

These are all characteristics exemplified in the duke.