Pseudo-symmetric pairs for Kac-Moody algebras

Vidas Regelskis, Bart Vlaar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces and real forms of complex Lie algebras, and are wellstudied in the context of symmetrizable Kac-Moody algebras. In this paper we study a generalization. Namely, we introduce the concept of a pseudoinvolution, 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 KacMoody 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.
Original languageEnglish
Title of host publicationHypergeometry, Integrability and Lie Theory - Virtual Conference Hypergeometry, Integrability and Lie Theory, 2020
EditorsErik Koelink, Stefan Kolb, Nicolai Reshetikhin, Bart Vlaar
PublisherAmerican Mathematical Society
Number of pages49
ISBN (Print)9781470465209
Publication statusPublished - 31 Aug 2022
EventVirtual conference on Hypergeometry, Integrability and Lie Theory, 2020 - Virtual, Online
Duration: 7 Dec 202011 Dec 2020

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


ConferenceVirtual conference on Hypergeometry, Integrability and Lie Theory, 2020
CityVirtual, Online


  • automorphism group
  • Kac-Moody algebras
  • restricted Weyl group
  • symmetric pairs


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