English

The bar involution for quantum symmetric pairs

Quantum Algebra 2016-02-01 v3 Representation Theory

Abstract

We construct a bar involution for quantum symmetric pair coideal subalgebras Bc,sB_{\mathbf{c},\mathbf{s}} corresponding to involutive automorphisms of the second kind of symmetrizable Kac-Moody algebras. To this end we give unified presentations of these algebras in terms of generators and relations extending previous results by G. Letzter and the second named author. We specify precisely the set of parameters c\mathbf{c} for which such an intrinsic bar involution exists.

Keywords

Cite

@article{arxiv.1409.5074,
  title  = {The bar involution for quantum symmetric pairs},
  author = {Martina Balagovic and Stefan Kolb},
  journal= {arXiv preprint arXiv:1409.5074},
  year   = {2016}
}

Comments

Minor revision: proof of Proposition 2.3 expanded; added new Remarks 2.8, 3.1, and 3.14; simplified base field in Section 3.3; typos corrected; final version; 25 pages

R2 v1 2026-06-22T05:59:04.933Z