engleski

Theta correspondence for p-adic dual pairs of type I

We describe explicitly the Howe correspondence for the symplectic-orthogonal and unitary dual pairs over a nonarchimedean local field of characteristic zero. More specif- ically, for every irreducible admissible representation of these groups, we find its first occurrence index in the theta correspondence and we describe, in terms of their Lang- lands parameters, the small theta lifts on all levels.

theta correspondence ; Weil representation ; metaplectic group

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