Induced representations of the group of diffeomorphisms of R3

Abstract

The class of representations of the diffeomorphism group introduced by Borisov (1979), based on SL(3,R); is extended to a class based on the universal covering group SL(3,R), and is generalised from the one-particle to the N-particle case. Earlier, the authors constructed induced representations of a local current group from little group representations that factor through the symmetric group SN, which is a discrete group. The present class of representations is obtained through an analogous construction first for the continuous group SL(3,R), and then for the semi-direct product group SL(3,R)N V-product SN.