Allusion in The Love Song of J. Alfred Prufrock
Eliot alludes to John the Baptist, a Biblical proponent of chastity who was supposedly beheaded at the request of King Herod’s wife, who displayed his head on a platter. Notice how Prufrock continues to denigrate himself by unfavorably comparing his own bald head to that of John the Baptist, stating that he is no such heroic figure, and his situation “no great matter.”
Eliot references “Works and Days” by the Greek poet Hesiod. In this didactic poem written in the 8th-century BCE, a farmer instructs his brother in how to live his life, urging him to work as hard as he himself does. Prufrock imagines other hands working harder than his own, leaving him time for a “hundred indecisions” and “visions and revisions” before he must ask the “overwhelming question.”
Lazarus of Bethany, aka Saint Lazarus, was purportedly raised from the dead by Jesus, who was a great friend of his. In the context of the poem, this allusion suggests that Prufrock either thinks or once thought of himself as a dead man, but that his love interest changes that. This unfortunately doesn't help with his social anxiety.
Prince Hamlet is the titular character of Shakespeare's famous play. In spite of his melancholy and his tendency toward dramatic monologue, Prufrock does not believe himself to be worthy of a starring role in life, instead relegating himself to a supporting, subservient role as an attendant lord.
Michelangelo was a famous Renaissance painter and sculptor whose most famous works include the "Statue of David" and the ceiling of the Sistine Chapel. That these women are discussing Michelangelo suggests that the poem's speaker has left the red-light district.
Notice how Eliot uses repetition in the poem to emphasize Prufrock's intellect. He wanders through the poem much as he does the dirty streets of the red-light district, bringing in images and allusions that aren't organic to the setting but are organic to his experience of it.