The distinction problems for Sp₄ and SO_3,3

Abstract

This paper studies the Prasad conjecture for the special orthogonal group \mathrm{SO}_{3,3}. Then we use the local theta correspondence between \mathrm{Sp}_{4} and \mathrm{O}(V) to study the \mathrm{Sp}_{4}-distinction problems over a quadratic field extension E/F and \dim V=4 or 6. Thus we can verify the Prasad conjecture for a square-integrable representation of \mathrm{Sp}_{4}(E).

Intertwining periods and distinction forp‐adic Galois symmetric pairs

“…We prove this relation in Theorem 8 for a certain class of generic irreducible representations of the classical group, that contains all irreducible generic principal series. Such results (and more) have been established in [38,39] for some small-rank classical groups.…”