Pseudo-symmetric pairs for Kac-Moody algebras

Vidas Regelskis, Bart Vlaar

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

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Abstract

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 publicationContemporary Mathematics. Virtual Conference Hypergeometry, Integrability and Lie Theory, 2020
EditorsErik Koelink, Stefan Kolb, Nicolai Reshetikhin, Bart Vlaar
PublisherAmerican Mathematical Society
Pages155-203
Number of pages49
Volume780
ISBN (Electronic) 978-1-4704-7134-7
ISBN (Print)978-1-4704-6520-9
DOIs
Publication statusPublished - 31 Aug 2022
EventVirtual conference on Hypergeometry, Integrability and Lie Theory, 2020 - Virtual, Online, Netherlands
Duration: 7 Dec 202011 Dec 2020

Publication series

NameContemporary Mathematics
Volume780
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Conference

ConferenceVirtual conference on Hypergeometry, Integrability and Lie Theory, 2020
Country/TerritoryNetherlands
CityVirtual, Online
Period7/12/2011/12/20

Keywords

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

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