Factor representations of diffeomorphism groups

Abstract

We give a new construction of seminite factor representations of the dieomorphism group of euclidean space. These representations are in canonical corre- spondence with the nite factor representations of the inductive limit unitary group. Hence, many of these representations are given in terms of quasi-free representations of the canonical commutation and anti-commutation relations. To establish this correspon- dence requires a generalization of complete positivity as developed in operator algebras. We also compare the asymptotic character formula for the unitary group with the ther- modynamic (N=V ) limit construction for dieomorphism group representations.