Department of Mathematics, University of Toronto, Toronto, Ontario M5S 3G3, Canada
Abstract:
In this paper we consider the theta correspondence between the sets and when is a nonarchimedean local field and . Our main theorem determines all the elements of that occur in the correspondence. The answer involves distinguished representations. As a corollary, we characterize all the elements of that occur in the theta correspondence between and . We also apply our main result to prove a case of a new conjecture of S.S. Kudla concerning the first occurrence of a representation in the theta correspondence.