Imaginary crystal bases for $U_q(\widehat{\mathfrak{sl}(2)})$-modules in category ${\mathcal{O}}_{\text{red,im}}^q$

Abstract

Recently we defined imaginary crystal bases for $U_q(\widehat{\mathfrak{sl}(2)})$- modules in category ${\mathcal{O}}_{\text{red,im}}^q$ and showed the existence of such bases for reduced quantized imaginary Verma modules for $U_q(\widehat{\mathfrak{sl}(2)})$. In this paper we show the existence of imaginary crystal basis for any object in the category ${\mathcal{O}}_{\text{red,im}}^q$.

13 pages. arXiv admin note: text overlap with arXiv:1509.00865, arXiv:0903.1062