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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 N 0 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.

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