The Prasad conjectures for $\mathrm{GS}{\mathrm{p}}_4$ and $\mathrm{PGS}{\mathrm{p}}_4$

Abstract

In this paper, we use the theta correspondence between $\mathrm{GS}{\mathrm{p}}_4$ and $\mathrm{GO}(\mathrm{V})$ to discuss the $\mathrm{GS}{\mathrm{p}}_4$-distinction problems over a quadratic field extension $E/F.$ With a similar strategy, we study the period for the pair $(\mathrm{GS}{\mathrm{p}}_4(\mathrm{E}),\mathrm{GS}{\mathrm{p}}_{1,1}(\mathrm{F})),$ where $\mathrm{GS}{\mathrm{p}}_{1,1}$ is the unique inner form of $\mathrm{GS}{\mathrm{p}}_4.$ Then we verify the Prasad conjecture for $\mathrm{PGS}{\mathrm{p}}_4(\mathrm{E})$.

We extend the results from tempered representations in the previous version (v1) to the generic representations. arXiv admin note: text overlap with arXiv:0706.0952 by other authors

References in corpus (3)

• Local Theta correspondence of Tempered Representations and Langlands parameters
• On distinguished square-integrable representations for Galois pairs and a conjecture of Prasad
• A New Proof to the Period Problems of GL(2)