Domination is hard to count.
I wouldn't go so far as to suggest artistic domination... unless its the realm of classical music in which the Germans and Austrians rule:biggrinjester: (and even there we have some very strong showing by the Italians, French, and Russians. The Italians probably dominated the Renaissance in Europe... but then at the same time the Persians were at their peak and China and Japan were no slackers.
Rather than "domination" I would suggest that the Latin-American contribution since mid-century cannot be ignored any more than that of the Americans for the 20th century as a whole.
Or looking closer to the present, Victorian literature. Why are our classics texts dominated by Victorian literature? Britain in the 19th century was a superpower: that's why people could begin to afford better things like novels. So writers could finally earn a better living. Actually I think it was easier for a Victorian writer to earn a living compared to now, because they didn't have TV or cinema then. But why Victorian??? Why not 18th century for instance?
Since when are "our" classics dominated by Victorian literature? The Three Musketeers, Les Miserables, Moby Dick, The Black and the Red, Nana, Don Quixote, Robinson Caruso, Tristram Shandy, The Brothers Karamazov, War and Peace, The Steppenwolf, The Magic Mountain, Gargantua and Pantagruel, Gulliver's Travels, Madame Bovary, In Search of Lost Time, Mlle de Maupin, Our Lady of the Flowers, Ulysses, The Sorrows of Young Werther, The Trial, etc... are all equally recognized as classics.
I wonder whether anyone has noticed that when there are fewer restraints on writing, the novel is more likely to become a classic?
Actually, Robert Louis Stevenson wrote an essay in which he claimed the opposite was true. The British writers, he argued, labored under a censorship of all sexuality. Stevenson compared the British writers of the 19th century to "muzzled dogs" and exclaimed, "What books Dickens could have written had he been permitted! Think of Thackery as unfettered as Flaubert or Balzac!... They give us a little box of toys and say to us, 'You musn't play with anything but these!' " Artists have almost always labored under censorship of one form or another. The strongest artists always find a way around the censors and still achieve something of genius.
Has anyone considered the possibility of fantasy taking over the literary world? I know they're more plot-driven than character-based, but epics seem to be timeless for some reason. Look at LOTR and the Greek epics. His Dark Materials may be a possible candidate. I know it's set in the past, but the idea of a tyrannous establishment seems to be an old plot device. And the wicked parents. In fantasy you get to exercise the creativity and wonder you don't get to do in fiction (stupid publishers) but if it has a fault the characters are not always realistic and can be too serious. If you think about it, Gothic tales and HP Lovecraft are making a comeback too, though they weren't considered serious fiction in their lifetime.
I think that there is a constant cycle of artists struggling against an establishment that has become fossilized and these same artists eventually becoming the establishment themselves. Undoubtedly, there are any number of artists... in literature, music, and the visual arts... who are achieving something of real merit by avoiding even attempting to work within the current system.

