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Conference Paper

Pseudo-symmetric pairs for Kac-Moody algebras

MPS-Authors
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Vlaar,  Bart
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1090/conm/780/15690
(Publisher version)

https://doi.org/10.48550/arXiv.2108.00260
(Preprint)

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Fulltext (public)

2108.00260.pdf
(Preprint), 769KB

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Citation

Regelskis, V., & Vlaar, B. (2022). Pseudo-symmetric pairs for Kac-Moody algebras. In E. Koelink, S. Kolb, N. Reschetichin, & B. Vlaar (Eds.), Hypergeometry, integrability and lie theory (pp. 155-203). Providence: American Mathematical Society.


Cite as: https://hdl.handle.net/21.11116/0000-000B-30A2-7
Abstract
Lie algebra involutions and their fixed-point subalgebras give rise to
symmetric spaces and real forms of complex Lie algebras, and are well-studied
in the context of symmetrizable Kac-Moody algebras. In this paper we study a
generalization. Namely, we introduce the concept of a pseudo-involution, an
automorphism which is only required to act involutively on a stable Cartan
subalgebra, and the concept of a pseudo-fixed-point subalgebra, a natural
substitute for the fixed-point subalgebra. In the symmetrizable Kac-Moody
setting, we give a comprehensive discussion of pseudo-involutions of the second
kind, the associated pseudo-fixed-point subalgebras, restricted root systems
and Weyl groups, in terms of generalizations of Satake diagrams.