Language translation is a notoriously difficult task for humans, let alone computers. But in trying to solve that problem Google has stumbled across a clever trick, that involves treating them like ...

Annals of Mathematics, Second Series, Vol. 167, No. 3 (May, 2008), pp. 945-991 (47 pages) We show that, on the level of derived categories, representations of the Lie algebra of a semisimple algebraic ...