In view of the controversy over Bob Dylan's Nobel, I would like to discuss two popular genres of literature that have not been represented--at least not so far as authors *primarily* known for them are concerned.
(1) What if the Nobel Prize for Literature were awarded to someone primarily known for science fiction? Yes, I know Doris Lessing wrote science fiction
https://en.wikipedia.org/wiki/Canopus_in_Argos but it is not *primarily* what she is known for. Likewise, even if one classifies *The Glass Bead Game* as science fiction, Hermann Hesse was not primarily a science fiction writer.
The science fiction writer who had the best chance for a Nobel was undoubtedly H. G. Wells, nominated four times.
http://www.nobelprize.org/nomination/archive/show_people.php?id=10075 Of more recent writers, I would have thought that Stanislaw Lem had the best chance, but looking at the nomination database, he was apparently never nominated, nor do I find the names of Bradbury, Asimov, Clarke, Heinlein, Butler... Nor could I find any nominations of Margaret Atwood or Ursula Le Guin (both of whom resist the science fiction label in any event).
(2) What if the Nobel Prize for Literature were awarded to someone primarily known for detective fiction? Although one of Patrick Modiano's novels involves a detective with amnesia, Modiano can't really be called a detective novelist. The detective fiction writer with the best chance was undoubtedly Georges Simenon, who was nominated seven times.
https://www.nobelprize.org/nomination/archive/show_people.php?id=12388 (I like Ted Gioia's "alternate Nobels" where Agatha Christie shares the 1966 Prize with Jorge Luis Borges,
http://www.greatbooksguide.com/nobel2.html but it was never likely to happen in the real world, though he does have Bob Dylan win in 1992...)