Fock space categorification, Soergel bimodules, and modular representation representation theory in type A

We give an executive summary of recent work with Ivan Losev, which connects modular representation theory in type A with a diagrammatic category of singular Soergel bimodules. As a consequence, various multiplicities in modular representation theory are encoded by p-Kazhdan-Lusztig polynomials. All this is in spite of the observation that the two sides of this story categorify different objects: one categorifies Fock space, while the other a space spanned by virtual partitions. We explain a magic trick due to Losev which allows one to compare this different categorical representations.

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