Intertwining periods and distinction for p-adic Galois symmetric pairs

TL;DR

This paper studies when certain p-adic Galois symmetric space representations are distinguished, providing new criteria, characterizations, and applications, especially for classical groups and Langlands functoriality.

Contribution

It introduces new sufficient conditions for the distinction of parabolically induced representations and characterizes distinction from cuspidal data, advancing understanding in p-adic Galois symmetric spaces.

Findings

New criteria for distinction of induced representations

Characterization of distinction from cuspidal representations

Applications to classical groups and Langlands functoriality

Abstract

We consider distinction of representations in the context of $p$-adic Galois symmetric spaces. We provide new sufficient conditions for distinction of parabolically induced representations in terms of similar conditions on the inducing data and deduce a characterization for distinction of representations parabolically induced from cuspidal. We explicate the results further for classical groups and give several applications, in particular, concerning the preservation of distinction via Langlands functoriality. We relate our results with a conjecture of Dipendra Prasad.