TY - GEN

T1 - Pseudo-symmetric pairs for Kac-Moody algebras

AU - Regelskis, Vidas

AU - Vlaar, Bart

N1 - © 2022 American Mathematical Society. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/

PY - 2022/8/31

Y1 - 2022/8/31

N2 - 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.

AB - 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.

KW - automorphism group

KW - Kac-Moody algebras

KW - restricted Weyl group

KW - symmetric pairs

UR - http://www.scopus.com/inward/record.url?scp=85137998601&partnerID=8YFLogxK

UR - https://arxiv.org/abs/2108.00260

U2 - 10.1090/conm/780/15690

DO - 10.1090/conm/780/15690

M3 - Conference contribution

AN - SCOPUS:85137998601

SN - 978-1-4704-6520-9

VL - 780

T3 - Contemporary Mathematics

SP - 155

EP - 203

BT - Contemporary Mathematics. Virtual Conference Hypergeometry, Integrability and Lie Theory, 2020

A2 - Koelink, Erik

A2 - Kolb, Stefan

A2 - Reshetikhin, Nicolai

A2 - Vlaar, Bart

PB - American Mathematical Society

T2 - Virtual conference on Hypergeometry, Integrability and Lie Theory, 2020

Y2 - 7 December 2020 through 11 December 2020

ER -