Higher Ext-groups and Relatively Supercuspidal Spectra

TL;DR

This paper investigates relatively supercuspidal representations within the relative Langlands program, utilizing top degree Ext-groups and duality to analyze their spectra, with specific examples in Galois and triple product cases.

Contribution

It introduces a novel approach using Ext-groups and duality to study relatively supercuspidal spectra, providing explicit examples in key cases.

Findings

Determined relatively supercuspidal spectra for Galois case.

Analyzed triple product case spectra.

Established Ext-groups as a tool for representation analysis.

Abstract

Relatively supercuspidal representations are analogue of supercuspidal representations in the relative Langlands program. This work studies relatively supercuspidal representations using top degree Ext-groups via the Schneider-Stuhler duality. As examples, the relatively supercuspidal spectra for the Galois case and the triple product case are determined.