Jacques-Marie-Émile Lacan was a French psychoanalyst, psychiatrist, and doctor, who made prominent contributions to the psychoanalytic movement. His yearly seminars, conducted in Paris from 1953 until his death in 1981, were a major influence in the French intellectual milieu of the 1960s and 1970s, particularly among post-structuralist thinkers.
Lacan's ideas centered on Freudian concepts such as the unconscious, the castration complex, the ego, focusing on identifications, and the centrality of language to subjectivity. His work was interdisciplinary, drawing on linguistics, philosophy, mathematics, amongst others. Although a controversial and divisive figure, Lacan is widely read in critical theory, literary studies, and twentieth-century French philosophy, as well as in the living practice of clinical psychoanalysis.
One of Lacan's better B-sides in need of A-list treatment. The available text is neater and more readable than some of the others. In short, the logic of fantasy is... grammatical. The ellipsis between Big A and little a shoots forth a subject marked with the ineradicable contingency of the unary trait, the One that could only become such by being repeated at least once, becoming a countable one, and another one, and so on. Look I'm extemporizing poorly because I'm unconvinced that any sort of summary is due. If you read S.XI and S.XVII in their respectable renditions you'll probably find what you're looking for. But the logic expounded here does provide a clinical bridge between those cultural/academic landmarks. And if you would care to plumb more of the perplexity of petit a, this one is for you. Fantasy regulates not only desire but perception and reality, and the a is the centerpiece of fantasy, staged for the Other, suspended on how the subject composes itself to either act-out the Other's directions (repetition), or pass to the act (sublimation).