The bar involution for quantum symmetric pairs -- hidden in plain sight

Abstract

We show that all quantum symmetric pair coideal subalgebras $B_\mathbf{c}$ of Kac-Moody type have a bar involution for a suitable choice of parameters $\mathbf{c}$. The proof relies on a generalized notion of quasi K-matrix. The proof does not involve an explicit presentation of $B_\mathbf{c}$ in terms of generators and relations.