I must confess that my go-to move in literary criticism is to take one work and compare it to another. In particular, I have frequently argued that an earlier work had been read by the author of a later work. That later author was then influenced by the earlier work. Many theorists of literary criticism reject this practice, and this rejection is related to the prohibition on the practice of arguing that something is present in a work because the author intended it to be there.
I recently studied Ralph Ellison's celebrated novel Invisible Man. In addition to attending to the text, I tried to read some of the criticism about it. That is an imposing task: Invisible Man holds the distinction of being the work of African American literature most studied by scholars. Indeed, Ellison spent much of the rest of his career commenting on the book himself and framing the terms of its interpretation. While I am not sure I have much to add, I thought I could weigh in with a comparison to Confederacy (naturally).
Unlike some of my comparisons, I do not claim that Toole was influenced by Invisible Man. (In point of fact, nowhere in the Toole Papers is Ellison or his work mentioned.) Instead, I would argue that Toole and Ellison were both influenced by the ideas of the Cambridge School of Classical Anthropology, the heirs to the ritual ideas contained in James Frazer's Golden Bough. Ellison, in his writings, was quite clear about the influence, citing T.S. Eliot and James Joyce as literary ancestors. He was also friends with Stanley Edgar Hyman, who was a leading critic familiar with that school.
Minor Parallels: During the section of Invisible Man where the invisible man (unnamed) disguises himself to look like Rinehart, he wears dark glasses in the nighttime. He can barely see, and what he does see has a green hue. In Confederacy, Burma Jones always wears dark glasses and can barely see. Confederacy has an entire theme of green (Ignatius's cap is green, Trixie's visor is green). What is the meaning of the green in each text?
Workplace Disasters: Both the invisible man and Ignatius are sources of disaster in the workplace. For the invisible man, when he chauffers a trustee and takes him to a brothel, he gets expelled from college, and on his first day of work at the paint factory, he manages to blow the place up. He is effective in his role as an inspirational speaker within the Brotherhood, but once he is alienated from the Brotherhood, he tries to sabotage it, and Harlem ends up in a race riot and conflagration.
Ignatius is also a source of disasters, though they are more minor and comic. At Levy Pants, he tries to foment an uprising of black workers, which fails. He eats nearly all of his hotdogs as a weenie vendor. His false letter at Levy Pants nearly gets Gus sued, but then allows him to stand up to his wife. The invisible man's failures are catastrophic and do not lead to improved relations within local social groups, while Ignatius's failures are comic, and they allow for changes in the local social order which improve the lives of other characters.
Wheels of History, and Cycles within Cycles: When the invisible man discusses with his colleague Hambro the Brotherhood's decision to sacrifice their position in Harlem, he says, "You mean the brakes must be put on the old wheel of history ... Or is it the little wheels within the wheel?" (chapter 23, page varies among editions). Related to that, the invisible man rejects the Brotherhood's view of a spiral of historical progress in favor of a theory of the boomerang of history: history is not progressive but cyclical, and it can whack you in the head.
In Confederacy, Ignatius sees himself being spun on Fortuna's wheel, but there are wheels within wheels. He writes: "So we see that even when Fortuna spins us downward, the wheel sometimes halts for a moment and we find ourselves in a good, small cycle within the larger bad cycle. The universe, of course, is based upon the principle of the circle within the circle. At the moment, I am in an inner circle. Of course, smaller circles within this circle are also possible." (1980 edition, p. 66). Ignatius sees history as rising and falling on the wheel of Fortuna. Related to these metaphors, both the invisible man and Ignatius reject leftist politics. This feature is so specific and so central to the meaning of each novel, if there was an actual influence by Ellison on Toole's thinking, it is here.
Boethius: Ellison even alludes to Boethius when he describes the musical tradition of the blues. In an essay first published in 1945 (Antioch Review 3.2, reprinted in Shadow and Act), Ellison writes that the source of the blues "is an impulse to keep the painful details and episodes of a brutal experience alive in one's aching consciousness, to finger its jagged grain, and to transcend it, not by the consolation of philosophy, but by squeezing from it a near-tragic, near-comic lyricism." Not by The Consolation of Philosophy. By comparison, within Confederacy, we do not have to go far to have Boethius's Consolation of Philosophy hit us in the head (sometimes literally).
Novelistic Style: Both Invisible Man and Confederacy reference many other works of literature and authors. Invisible Man employs a dark, existentialist humor, while Confederacy's humor is a farce in the much more straightforward, Greek New Comedy style. Barbara Foley, in her study Wrestling with the Left, observes that in the Invisible Man "the invisible man is launched into his career as the protagonist of a half-picaresque, half-bildungsroman memoir" (157). This description could be applied to Ignatius in Confederacy, except in the case of Ignatius one might question whether there is any Bildung going on.
Observing from the Periphery: The invisible man in Invisible Man ends up outside of history, writing his account from a well-lit hideaway in New York City. Ignatius Reilly also sees himself as being on the edge of his society looking from that edge inward to criticize it.
Much Deeper Connections: The invisible man is an example of the sacrificial god-king from Frazer's Golden Bough. Ignatius Reilly is a carnival / saturnalian Lord of Misrule, which is a comic and carnival scapegoat version of that dying and resurrected god.
Thesis: Compare Invisible Man and A Confederacy of Dunces. Their authors both drew on a Cambridge School tradition of meaning. I have found a lot, and there is a lot more to uncover.