Distinction of the Steinberg representation

TL;DR

This paper proves a conjecture regarding when the Steinberg representation is distinguished in symmetric spaces formed by G(E)/G(F), with G split over F and E/F an unramified quadratic extension.

Contribution

It establishes the proof of Dipendra Prasad's conjecture on the distinction of the Steinberg representation for specific symmetric spaces.

Findings

Proof of Prasad's conjecture confirmed.

Characterization of distinguished Steinberg representations achieved.

Applicable to split reductive groups over non-archimedean fields.

Abstract

We prove Dipendra Prasad's conjecture on the distinction of the Steinberg representation for symmetric spaces of the form G(E)/G(F), where G is a split reductive group defined over F and E/F an unramified quadratic extension of non-archimedean local fields.