Unitarising measures for Kac-Moody algebras
Abstract
Given a compact connected Lie group $G$ with dual Coxeter number $\check h$ and a level $κ0$. We prove that $ν_κ$ is characterised by a covariance property making rigorous sense of the formal path integral ``$\mathrm dν_κ(γ)=e^{-\checkκ\mathscr{S}(γ)}Dγ$", where $Dγ$ is the non-existent Haar measure on the loop group and $\mathscr S$ is a Kähler potential for the right-invariant Kac--Moody metric. Infinitesimally, the covariance formula prescribes the Shapovalov forms of the Kac--Moody representations.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Advanced Algebra and Geometry
Geometry and complex manifolds
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 5 February 2026
- Language
- EN
- Document type
- Preprint