I will talk about the problem of classifying blocks of category O for the general linear Lie superalgebra, both up to Morita equivalence and up to gradable derived equivalence. The analogous problem for a semisimple Lie algebra is usually approached via Soergel’s theory of graded category O. The main point of the talk will be to explain an appropriate substitute in the super case. This comes from the W-algebra associated to the principal nilpotent orbit in g. Categorical Kac-Moody actions in the sense of Rouquier also play a role.

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