Pseudo-symmetric pairs for Kac-Moody algebras

Vidas Regelskis, Bart Vlaar

Published 2021-07-31Version 1

Involutive automorphisms of the second kind of Kac-Moody algebras and their fixed-point subalgebras can be q-deformed following Letzter and Kolb. These q-deformed algebras play a major role in the theory of the reflection equation. Essentially the same constructions can be made in a larger setting, where the automorphism is required to act involutively only on a stable Cartan subalgebra. We give a comprehensive Lie- and Coxeter-theoretic discussion of pseudo-involutions, pseudo-fixed-point subalgebras, including a survey of the associated restricted root systems and Weyl groups in the Kac-Moody setting, in terms of generalizations of Satake diagrams.