## The bar involution for quantum symmetric pairs

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- by Martina Balagović and Stefan Kolb
- Represent. Theory
**19**(2015), 186-210 - DOI: https://doi.org/10.1090/ert/469
- Published electronically: October 23, 2015
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## Abstract:

We construct a bar involution for quantum symmetric pair coideal subalgebras $B_{\mathbf {c},\mathbf {s}}$ 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 $\mathbf {c}$ for which such an intrinsic bar involution exists.## References

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## Bibliographic Information

**Martina Balagović**- Affiliation: School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
- MR Author ID: 919905
- Email: martina.balagovic@newcastle.ac.uk
**Stefan Kolb**- Affiliation: School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
- MR Author ID: 699246
- Email: stefan.kolb@newcastle.ac.uk
- Received by editor(s): October 15, 2014
- Received by editor(s) in revised form: January 7, 2015, and September 14, 2015
- Published electronically: October 23, 2015
- Additional Notes: This research was supported by EPSRC grant EP/K025384/1
- © Copyright 2015 American Mathematical Society
- Journal: Represent. Theory
**19**(2015), 186-210 - MSC (2010): Primary 17B37, 81R50
- DOI: https://doi.org/10.1090/ert/469
- MathSciNet review: 3414769