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Un exercice sur $$GSp(4,F)$$ et les représentations de Weil. (An exercise on $$GSp(4,F)$$ and the Weil representations). (French) Zbl 0635.22016
Consider the dual reductive pair $$(G,G')=(GSp(4,F),GO^+(q))$$ in GSp(24,F), where q is the split quadratic form in 6 variables. Here F is a non archimedean local field of characteristic $$\neq 2$$. The Weil representation of GSp(24,F) determines a correspondence between irreducible representations of G and irreducible representations of G’. In the paper this correspondence is computed explicitly for the irreducible constituents of the representations of G induced from a supercuspidal representation of the standard parabolic subgroup of G corresponding to the long root. The Howe conjecture is shown to be valid for these representations.
Reviewer: J.G.M.Mars

##### MSC:
 22E50 Representations of Lie and linear algebraic groups over local fields 11F70 Representation-theoretic methods; automorphic representations over local and global fields
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##### References:
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