On branching laws of Speh representations
Abstrak
In this paper, we consider the branching law of the Speh representation $\mathrm{Sp}(π,n+l)$ of $\mathrm{GL}_{2n+2l}$ with respect to the block diagonal subgroup $\mathrm{GL}_n\times\mathrm{GL}_{n+2l}$ for any irreducible generic representation $π$ of $\mathrm{GL}_2$ over any $p$-adic field. We use the Shalika model of $\mathrm{Sp}(π,n)$ to construct certain zeta integrals, which were defined by Ginzburg and Kaplan independently, and study them. Finally, using these zeta integrals, we obtain a nonzero $\mathrm{GL}_n\times\mathrm{GL}_{n+2l}$-map from $\mathrm{Sp}(π,n+l)$ to $τ\boxtimesτ^\veeχ_π\times\mathrm{Sp}(π, l)$ for any irreducible representation $τ$ of $\mathrm{GL}_n$. These results form part of the local theory of the Miyawaki lifting for unitary groups.
Penulis (1)
Nozomi Ito
Akses Cepat
- Tahun Terbit
- 2021
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓