Distinguished Regular Supercuspidal Representations and Inductive Constructions of Representations

TL;DR

This paper explores the theory of distinguished regular supercuspidal representations and examines how the correspondence between regular characters and these representations resembles induction processes.

Contribution

It develops the theory of distinguished regular supercuspidal representations and clarifies their relationship with regular characters and induction methods.

Findings

Established a framework for distinguished regular supercuspidal representations.

Showed the analogy between the correspondence and induction processes.

Provided new insights into the structure of supercuspidal representations.

Abstract

This paper develops the theory of distinguished regular supercuspidal representations, and it highlights how the correspondence between regular characters and regular supercuspidal representations resembles induction in certain ways.