, Volume 69, Issue 1, pp 25-45

Degenerate principal series and invariant distributions

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Abstract

In this article we give a description of the tempered distributions on a matrix spaceM m,n(R) which are invariant under the linear action of an orthogonal groupO(p, q),p+q=m. We also determine the points of reducibility of the degenerate principal series of the metaplectic group Mp(n,R) induced from a character of the maximal parabolic with GL(n,R) as Levi factor. Finally, we identify the representation of MP(n,R) which is associated to the trivial representation ofO(p, q) under the archimedean theta correspondence.

Partially supported by NSF Grant DMS-87-04375.
Partially supported by NSF Grant DMS-84-01947.