Natural Elements of Center of Generalized Quantum Groups

TL;DR

This paper identifies elements in the center of generalized quantum groups related to their finite-dimensional modules and conjectures these elements form a basis for the entire center.

Contribution

It introduces specific elements in the (skew) center of generalized quantum groups and proposes a conjecture about their basis-forming property.

Findings

Elements in the (skew) center linked to finite-dimensional modules

A conjecture that these elements form a basis of the center

Foundation for future proof or exploration of the conjecture

Abstract

This paper gives elements in the (skew) center of the generalized quantum group corresponding to its irreducible finite dimensional modules. Finally we give a conjecture stating that those must form a basis of the center.