Uniqueness of Ginzburg-Rallis models: the Archimedean case

TL;DR

This paper proves the uniqueness of Ginzburg-Rallis models over Archimedean fields using a novel descent method involving geometric concepts like metrical properness and unipotent incompatibility.

Contribution

It introduces a new descent argument based on geometric notions to establish the uniqueness of Ginzburg-Rallis models in the Archimedean setting.

Findings

Proves the uniqueness of Ginzburg-Rallis models in the Archimedean case.

Develops a new descent technique using geometric notions.

Provides a framework potentially applicable to other models.

Abstract

In this paper, we prove the uniqueness of Ginzburg-Rallis models in the archimedean case. As a key ingredient, we introduce a new descent argument based on two geometric notions attached to submanifolds, which we call metrical properness and unipotent $\chi$-incompatibility.