Diagram automorphisms and canonical bases for quantum affine algebras, II.

Let U q − be the negative part of the quantum enveloping algebra, and σ the algebra automorphism on U q − induced from a diagram automorphism. Let U _ q − be the quantum algebra obtained from σ , and B ˜ (resp. B _ ˜) the canonical signed basis of U q − (resp. U _ q −). Assume that U q − is simply-laced of finite or affine type. In our previous papers [10] , [11] , we have proved by an elementary method, that there exists a natural bijection B ˜ σ ≃ B _ ˜ in the case where σ is admissible. In this paper, we show that such a bijection exists even if σ is not admissible, possibly except some small rank cases. [ABSTRACT FROM AUTHOR]