The speaker
The speaker spends much of the poem skipping around in time, not focusing on himself, but he does specifically describe the joy the Aquarium brought him in his childhood, which suggests that he is now an older man. At one point he crouches in front of a TV, watching coverage on the Civil Rights Movement.
Colonel Shaw
Colonel Shaw is a historical figure, a young white soldier for the Union who— at first reluctantly—accepted command of an all-black regiment during the Civil War. He encouraged his men to join in a boycott so black soldiers would be paid as much as the white ones. He also wrote in protest of war crimes perpetrated by the Union against the mostly black population of Darien, Georgia. The narrator focuses heavily on this character and seems impressed by his righteousness.
Colonel Shaw's father
Colonel Shaw's father is proud of his son; he believes that there is no higher tribute than being buried with one's men for a rightful cause. However, Lowell quotes him using a derogatory slur to refer to the black soldiers. This character represents how a modern perspective complicates the abolitionists; even the ones who worked to further the rights of Black people were racist by today's standards.
William James
This philosopher attended the dedication of St. Gauden's relief and believed he could almost see the soldiers on the monument breathe. His feelings about the monument contrast with modern attitudes; what seemed so real and poignant to him now feels out of place in Boston.