Euler systems and relative Satake isomorphism

TL;DR

This paper links the relative Langlands program's unramified Plancherel formula to the construction of Euler systems, providing a unified approach and introducing a new split anticyclotomic Euler system in the twisted Friedberg--Jacquet setting.

Contribution

It introduces a novel method using the relative Langlands framework to construct Euler systems and presents a new split anticyclotomic Euler system.

Findings

Unified construction of known Euler systems

New split anticyclotomic Euler system in twisted Friedberg--Jacquet setting

Connection between Plancherel formula and Euler system norm relations

Abstract

We explain how the unramified Plancherel formula in the relative Langlands program gives a natural way of constructing test vectors which satisfy the tame norm relations of an Euler system. This uniformly recovers many of the known Euler systems, and in the twisted Friedberg--Jacquet setting, we produce a new split anticyclotomic Euler system.