A new method for constructing factorisable representations for current groups and current algebras

Abstract

Let C_e^∞ (Rⁿ ,G) denote the group of infinitely differentiable maps from n-dimensional Euclidean space into a simply connected and connected Lie group, which have compact support. This paper introduces a class of factorisable unitary representations of C_e^∞ (Rⁿ ,G) with the property that the unitary operator U_ƒ corresponding to a function ƒ in C_e^∞ (Rⁿ ,G) depends not only on ƒ, but also on the derivatives of ƒ up to a certain order. In particular these representations can not be extended to the group of all continuous functions from Rⁿ to G with compact support.