The dual pair $\mathrm {Aut}(C)\times F_{4}$ (p-adic case)

Karasiewicz, Edmund  ; Savin, Gordan

Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e174

Résumé

We study the local theta correspondence for dual pairs of the form $\mathrm {Aut}(C)\times F_{4}$ over a p-adic field, where C is a composition algebra of dimension $2$ or $4$, by restricting the minimal representation of a group of type E. We investigate this restriction through the computation of maximal parabolic Jacquet modules and the Fourier–Jacobi functor.As a consequence of our results, we prove a multiplicity one result for the $\mathrm {Spin}(9)$-invariant linear functionals of irreducible representations of $F_{4}$ and classify the $\mathrm {Spin}(9)$-distinguished representations.

Détail

DOI : 10.1017/fms.2025.10108

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