On Hecke algebras and simple supercuspidal representations for Sp(4,F)

TL;DR

This paper explores the relationship between Hecke algebras and simple supercuspidal representations in the context of Sp(4,F), extending the understanding of Bernstein components in p-adic groups.

Contribution

It investigates Bernstein components for Sp(4,F) linked to principal series induced from simple supercuspidal representations, providing new insights into their structure.

Findings

Characterization of Bernstein components for Sp(4,F)

Connection between Hecke algebras and supercuspidal representations

Extension of Borel's result to specific Bernstein components

Abstract

A well known result of Borel says that the category of modules over the Iwahori-Hecke algebra of a semisimple p-adic group G describes the Bernstein component associated to the unramified principal series of G. We consider Bernstein components for Sp(4,F) associated to principal series induced from simple supercuspidal representations.