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arXiv · 1810.10503

Derived representation theory of Lie algebras and stable homotopy categorification of $sl_k$

Po Hu·Igor Kriz·Petr Somberg
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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, $gl_n(S)$-Verma modules and their duals, Harish-Chandra pairs and Zuckermann functors. As an application, we construct a Khovanov $sl_k$-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.

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Po Hu, Igor Kriz, Petr Somberg. 2018-10-24. Derived representation theory of Lie algebras and stable homotopy categorification of $sl_k$. https://arxiv.org/abs/1810.10503

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