Kostant-Lusztig $\mathbb A$-bases of Multiparameter Quantum Groups

TL;DR

This paper investigates the Kostant-Lusztig $ ext{A}$-bases in multiparameter quantum groups, employing duality of the universal $R$-matrix pairing to facilitate calculations, notably for the $G_2$ type.

Contribution

It introduces a method leveraging the duality of the universal $R$-matrix pairing to simplify the study of $ ext{A}$-bases in multiparameter quantum groups, especially for complex types.

Findings

Simplified calculations for $G_2$-type quantum groups.

Established duality approach for $ ext{A}$-bases.

Enhanced understanding of the structure of multiparameter quantum groups.

Abstract

We study the Kostant-Lusztig $\mathbb A$-base of the multiparameter quantum groups. To simplify calculations, especially for $G_2$-type, we utilize the duality of the pairing of the universal $R$-matrix.