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I have been trying to learn about the representation theory of Kac-Moody algebras in positive characteristic. However, my usual reference for the subject (Infinite dimensional Lie algebras by Kac) assumes throughout that the field has characteristic $0$.

Trying to find new references online has lead to some interesting resources, but so far they all deal with the related group-theoretic structures e.g. linear algebraic groups (over a field of characteristic $p>0$) and the corresponding restricted Lie algebras.

Does anyone know where I could find an account of the representation theory of Kac-Moody algebras over a field of characteristic $p>0$?

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  • $\begingroup$ This is not very precise, but Pianzola and his collaborators have done a lot of work on the relationship between twistings of Kac-Moody algebras and groups and étale cohomology with coefficients in groups. Perhaps an adaptation of these ideas to fppf cohomology might work ? $\endgroup$
    – Dat Minh Ha
    Commented Feb 17 at 1:06

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