The bar involution for quantum symmetric pairs

Balagović, Martina; Kolb, Stefan

doi:10.1090/ert/469

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.

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