Derived representation theory of Lie algebras and stable homotopy categorification of slk

Abstract

We set up foundations of representation theory over S, the sphere spectrum, which is the “initial ring” of stable homotopy theory. In particular, we treat S-Lie algebras and their representations, characters, gln(S)-Verma modules and their duals, Harish-Chandra pairs and Zuckermann functors. As an application, we construct a Khovanov slk-stable homotopy type with a large prime hypothesis, which is a new link invariant, using a stable homotopy analogue of the method of J. Sussan.