Canonical bases of the modified quantized enveloping algebras of type $A_{2}$

Abstract

The modified quantized enveloping algebra $\dot{\mathbf{U}}$ has a remarkable canonical basis, which was introduced by Lusztig. In this paper, we give an explicit description of all elements of the canonical basis of $\dot{\mathbf{U}}$ for type $A_{2}$.

we give an explicit description of all elements of the canonical basis of modified quantized algebras for type A_2