Quasiregular representations of the infinite-dimensional nilpotent group

摘要

In the present work an analog of the quasiregular representation which is well known for locally-compact groups is constructed for the nilpotent infinite-dimensional group B-0(N) and a criterion for its irreducibility is presented. This construction uses the infinite tensor product of arbitrary Gaussian measures in the spaces R-m with m > 1 extending in a rather subtle way previous work of the second author for the infinite tensor product of one-dimensional Gaussian measures. (c) 2006 Elsevier Inc. All rights reserved.