A character formula for certain representations of loop groups based on non-simply connected Lie groups

TL;DR

This paper extends the Kac-Weyl character formula to certain representations of loop groups derived from non-simply connected Lie groups, providing a broader understanding of their characters.

Contribution

It generalizes the Kac-Weyl character formula to loop groups associated with non-simply connected Lie groups, filling a gap in representation theory.

Findings

Derived explicit character formulas for these representations

Extended the applicability of the Kac-Weyl formula

Provided new tools for studying non-simply connected Lie group representations

Abstract

I calculate characters of certain representations of loop groups based on non simply connected Lie groups. This gives a generalization of the Kac-Weyl character formula.