Stability of canonical bases of irreducible finite type of real rank one

It has been known since their birth in Bao and Wang’s work that the ı \imath canonical bases of ı \imath quantum groups are not stable in general. In the author’s previous work, the stability of ı \imath canonical bases of certain quasi-split types turned out to be closely related to the theory of ı \imath crystals. In this paper, we prove the stability of ı \imath canonical bases of irreducible finite type of real rank 1 1 , for which the theory of ı \imath crystals has not been developed, by means of global and local crystal bases.