# The bar involution for quantum symmetric pairs -- hidden in plain sight

@inproceedings{Kolb2021TheBI, title={The bar involution for quantum symmetric pairs -- hidden in plain sight}, author={Stefan Kolb}, year={2021} }

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 K-matrix. The proof does not involve an explicit presentation of Bc in terms of generators and relations.

## 6 Citations

Defining relations of quantum symmetric pair coideal subalgebras

- MathematicsForum of Mathematics, Sigma
- 2021

Abstract We explicitly determine the defining relations of all quantum symmetric pair coideal subalgebras of quantised enveloping algebras of Kac–Moody type. Our methods are based on star products on…

Quantum symmetric pairs

- Mathematics
- 2021

This is a survey of some recent progress on quantum symmetric pairs and applications. The topics include quasi K-matrices, ıSchur duality, canonical bases, super Kazhdan-Lusztig theory, ıHall…

Pseudo-symmetric pairs for Kac-Moody algebras

- Mathematics
- 2021

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.…

Universal K-matrices for quantum Kac-Moody algebras

- MathematicsRepresentation Theory of the American Mathematical Society
- 2022

We introduce the notion of a cylindrical bialgebra, which is a quasitriangular bialgebra
H
H
endowed with a universal K-matrix, i.e., a universal solution of a generalized reflection…

Rational K-matrices for finite-dimensional representations of quantum affine algebras

- Mathematics
- 2022

. Let g be a complex simple Lie algebra. We prove that every ﬁnite-dimensional representation of the (untwisted) quantum aﬃne algebra U q L g gives rise to a family of spectral K-matrices, namely…

Stability of $\imath$canonical bases of irreducible finite type of real rank one

- Mathematics
- 2022

. It has been known since their birth in Bao and Wang’s work that the ı canonical bases of ı quantum groups are not stable in general. In the author’s previ-ous work, the stability of ı canonical…

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