The generalized doubling method: $(k,c)$ models

TL;DR

This paper introduces a new class of local models called $(k,c)$ models for generalized Speh representations, proving their uniqueness and supporting the Eulerian property of the generalized doubling integral.

Contribution

It constructs and analyzes $(k,c)$ models in a local setting, providing a key uniqueness theorem crucial for the generalized doubling method.

Findings

Established a family of $(k,c)$ representations

Proved a uniqueness theorem for these models

Supported the Eulerian property of the generalized doubling integral

Abstract

One of the key ingredients in the recent construction of the generalized doubling method is a new class of models, called $(k,c)$ models, for local components of generalized Speh representations. We construct a family of $(k,c)$ representations, in a purely local setting, and discuss their realizations using inductive formulas. Our main result is a uniqueness theorem which is essential for the proof that the generalized doubling integral is Eulerian.