• Corpus ID: 236772084

# Pseudo-symmetric pairs for Kac-Moody algebras

@inproceedings{Regelskis2021PseudosymmetricPF,
title={Pseudo-symmetric pairs for Kac-Moody algebras},
author={Vidas Regelskis and Bart Vlaar},
year={2021}
}
• Published 31 July 2021
• Mathematics
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 KacMoody algebras. In this paper we propose 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 fixedpoint subalgebra. In…
1 Citations

## Tables from this paper

Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras
• Mathematics
• 2022
. We deﬁne a boundary analogue of the Kang-Kashiwara-Kim-Oh generalized Schur-Weyl dualities between quantum aﬃne algebras and Khovanov-Lauda-Rouquier (KLR) algebras. Let g be a complex simple Lie

## References

SHOWING 1-10 OF 79 REFERENCES
The bar involution for quantum symmetric pairs -- hidden in plain sight
We show that all quantum symmetric pair coideal subalgebras Bc of Kac-Moody type have a bar involution for a suitable choice of parameters c. The proof relies on a generalized notion of quasi
The Component Group of the Automorphism Group of a Simple Lie Algebra and the Splitting of the Corresponding Short Exact Sequence
Let g be a simple Lie algebra of finite dimension over K ∈ {R, C} and Aut(g) the finite-dimensional Lie group of its automorphisms. We will calculate the component group π0(Aut(g)) = Aut(g)/ Aut(g)0
Asymptotic boundary KZB operators and quantum Calogero-Moser spin chains
• Mathematics
• 2020
Asymptotic boundary KZB equations describe the consistency conditions of degenerations of correlation functions for boundary Wess-Zumino-Witten-Novikov conformal field theory on a cylinder. In the
Universal k-matrices for quantum Kac-Moody algebras
• Mathematics
• 2020
We define the notion of an \emph{almost cylindrical} bialgebra, which is roughly a quasitriangular bialgebra endowed with a universal solution of a {twisted} reflection equation, called a {twisted}
Hall algebras and quantum symmetric pairs of Kac-Moody type
• Mathematics
• 2020
We extend our ıHall algebra construction from acyclic to arbitrary ıquivers, where the ıquiver algebras are infinite-dimensional 1-Gorenstein in general. Then we establish an injective homomorphism
N-point spherical functions and asymptotic boundary KZB equations
• Mathematics
Inventiones mathematicae
• 2022
Let $G$ be a split real connected Lie group with finite center. In the first part of the paper we define and study formal elementary spherical functions. They are formal power series analogues of
Sous-algèbres de Cartan des algèbres de Kac-Moody affines réelles presque compactes.
• Mathematics
• 2006
Almost compact real forms of affine Kac-Moody Lie algebras have been already classified [J. Algebra 267, 443-513]. In the present paper, we study the conjugate classes of their Cartan subalgebras
Outer automorphism groups of simple Lie algebras and symmetries of painted diagrams
• Mathematics
• 2017
Let g be a simple Lie algebra. Let Aut(g) be the group of all automorphisms on g, and let Int(g) be its identity component. The outer automorphism group of g is defined as Aut(g)/Int(g). If g is