Compatibility of Drinfeld presentations and $q$-characters for affine Kac-Moody quantum symmetric pairs: quasi-split case

Abstract

Let $(\mathbf{U},{\mathbf{U}}^{ı})$ be a quasi-split affine quantum symmetric pair of type $\mathsf{AIII}$. This case is of particular interest thanks to the existence of geometric realizations and Schur--Weyl dualities. We establish factorization and coproduct formulae for the Drinfeld--Cartan series ${\mathbf{\Theta }}_i(z)$ in the Lu--Pan--Wang--Zhang `new Drinfeld'-style presentation, generalizing the split type results from [Prz23, LP25a]. As an application, we construct a boundary analogue of the $q$-character map, and show that it is compatible with Frenkel and Reshetikhin's original $q$-character homomorphism.

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