The bar involution for quantum symmetric pairs

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.

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

References in corpus (2)

• A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs
• Geometric Schur duality of classical type

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