تقرير
The Dual Pair $\mathrm{Aut}(C)\times F_{4}$ ($p$-adic case)
| العنوان: | The Dual Pair $\mathrm{Aut}(C)\times F_{4}$ ($p$-adic case) |
|---|---|
| المؤلفون: | Karasiewicz, Edmund, Savin, Gordan |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, Mathematics - Number Theory, 11F27, 22E50 |
| الوصف: | 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. Comment: 35 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.02853 |
| رقم الأكسشن: | edsarx.2312.02853 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |