Symbolism, Imagery, Allegory
Literary analysis pro-tip, ladies and germs: if a novel opens at the opera, you know that things are going to be theatrical.
We don't mean theatrical as in bombastic, or everyone screaming and falling to their knees, or even full of monologues. We mean "of the theater." And what does everyone do at the theater? Well, they either watch or they perform.
"Watching" and "performing" are two of the things (maybe the only two things) that everyone in The Age of Innocence does. Certainly we know that everyone is watching everyone, all the time, and talking about each other behind their backs. But everyone is also playing a part: and usually, boringly, that part is The Good Member of New York High Society.
Take Julius Beaufort, who masks his illegal wheelings and dealings behind a façade:
"…these domestic activities were privately performed, and he presented to the world the appearance of a careless and hospitable millionaire strolling into his own drawing-room with the detachment of an invited guest." (3.5)
Or take Newland and Ellen, who need to perform the role of Two People Not Hopelessly Smitten By Each Other. In fact, Newland and Ellen have to bury their feelings so deeply that they rely on the performers in plays to bring their emotions to life. Take the Shaughraun, and Newland's remembrance of the play when he watches Ellen at the pier, hoping she'll turn around:
"Archer, as he watched, remembered the scene in the Shaughraun, and Montague lifting Ada Dyas's ribbon to his lips without her knowing that he was in the room." (21.33)
In fact, each play that the good folks of New York City watch seems to be tied up in some way to the action in The Age of Innocence. This is in no way an accident. We know about the tragic ribbon-kissing in the Shaughraun, and remember how Faust is about a dude making a pretty epic deal with the devil. Hmm, a deal with the devil? Like, for example, a deal that would trade happiness and fulfillment for material comfort and social conformity? That kind of Newland Archer-style deal?