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

TL;DR

This paper provides an explicit description of the canonical basis of the modified quantized enveloping algebra for type A2, enhancing understanding of its structure and basis elements.

Contribution

It offers a complete explicit characterization of the canonical basis for the type A2 modified quantized enveloping algebra, a previously less detailed aspect.

Findings

Explicit description of all canonical basis elements for type A2

Clarification of the structure of the canonical basis in this setting

Advancement in understanding the algebra's basis elements

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 $A_{2}$.