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

Edmund Karasiewicz; Gordan Savin

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arXiv · 2312.02853

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

Edmund Karasiewicz·Gordan Savin

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Abstract

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.

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BibTeX RIS

Edmund Karasiewicz, Gordan Savin. 2023-12-05. The Dual Pair $\mathrm{Aut}(C)\times F_{4}$ ($p$-adic case). https://arxiv.org/abs/2312.02853

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