Theta functions and arithmetic quotients of loop groups (Q2391582)

The author shows that isomorphism classes of certain metrized vector bundles over \(\operatorname{Spec}\mathbb{Z}[t,t^{-1}]\) can be parameterized using arithmetic quotients of loop groups (with a certain additional datum called covolume theory). These quotients are used to define an asymptotic version of theta functions. The author gives various interpretations for this asymptotic theta function and proves some convergence results. Finally, the author discusses an extension of this function to loop symplectic groups, a relation of this function with loop Heisenberg groups and gives an asymptotic multiplication formula.