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The bar involution for quantum symmetric pairs


Authors: Martina Balagović and Stefan Kolb
Journal: Represent. Theory 19 (2015), 186-210
MSC (2010): Primary 17B37, 81R50
DOI: https://doi.org/10.1090/ert/469
Published electronically: October 23, 2015
MathSciNet review: 3414769
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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.


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Additional Information

Martina Balagović
Affiliation: School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
Email: martina.balagovic@newcastle.ac.uk

Stefan Kolb
Affiliation: School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
Email: stefan.kolb@newcastle.ac.uk

DOI: https://doi.org/10.1090/ert/469
Keywords: Quantum groups, bar involution, coideal subalgebras, quantum symmetric pairs
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
Article copyright: © Copyright 2015 American Mathematical Society

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