Euler systems and relative Satake isomorphism

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.

32 pages