Finite Young wall model for representations of $$\imath $$ quantum group $${\textbf{U}}^{\jmath }$$

Abstract

We construct a finite Young wall model for a certain irreducible module over \(\imath \)quantum group \({\textbf{U}}^{\jmath }\). Moreover, we show that this irreducible module is a highest weight module and is determined by a crystal structure on the set of finite Young walls.