Addendum to "Quivers with loops and perverse sheaves"

TL;DR

This paper proves a character formula for a Hopf algebra generalizing quantum groups and for simple modules related to dominant weights, extending previous work in the field.

Contribution

It introduces a new character formula applicable to a broad class of Hopf algebras and their modules, generalizing prior quantum group results.

Findings

Established a character formula for the Hopf algebra in question

Extended the formula to simple modules associated with dominant integral weights

Generalized quantum group character formulas to a wider algebraic context

Abstract

We prove a character formula for the Hopf algebra defined in arXiv:1401.5302 that generalizes quantum groups, as well as for the simple modules associated to dominant integral weights defined in arXiv:1403.0846.