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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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