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

Abstract

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

26 pages, minor modification in Introduction