engleski

Theta lifts of generic representations for dual pairs (text {;;;Sp};;;_{;;;2n};;;, text {;;;O};;;(V))

We determine the occurrence and explicitly describe the theta lifts on all levels of all the irreducible generic representations for the dual pair of groups (Sp_2n, O(V)) defined over a local nonarchimedean field F of characteristic 0. As a direct application of our results, we are able to produce a series of non-generic unitarizable representations of these groups.

p-adic groups ; generic representations ; theta correspondence

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