iCanonical basis arising from quasi-split rank one iquantum group

Abstract

We compute icanonical basis of the quasi-split rank one modified iquantum group, by obtaining explicit transition matrices among the icanonical basis, monomial basis, and standardized canonical basis; all these bases can be naturally categorified. These transition matrices follow from their counterparts computed in this paper among the icanonical basis, monomial basis, and canonical basis on simple finite-dimensional modules of quantum ${\mathfrak{sl}}_3$.

arXiv commentv1: 54 pages