Models of representations and Langlands functoriality

TL;DR

This paper investigates the relationship between advanced models of representations in automorphic forms and two key functorial operations, base change and automorphic induction, for specific classes of representations of general linear groups.

Contribution

It introduces a new analysis of how Klyachko and degenerate Whittaker models interact with base change and automorphic induction for unitarizable and ladder representations.

Findings

Established connections between models and functorial operations.

Extended understanding of representation behavior under functorial transfers.

Provided new insights into the structure of unitarizable and ladder representations.

Abstract

In this article we explore the interplay between two generalizations of the Whittaker model, namely the Klyachko models and the degenerate Whittaker models, and two functorial constructions, namely base change and automorphic induction, for the class of unitarizable and ladder representations of the general linear groups.